 Hello and welcome to the session. The given question says, using the quadratic formula, solve the equation a square b square x square minus 4 times of b raised to the power 4 minus 3 times of a raised to the power 4 into x minus 12 a square into b square is equal to 0. First, let us learn that if we have a quadratic equation of the type, px square plus qx less r is equal to 0, then how do we find its roots? The formula to find the roots of this equation is minus q plus minus root over d divided by 2 times of p where d is the discriminant and its value is equal to q square minus 4 times of p into r. So, this is the key idea we are going to use in this problem to solve it. Let us now begin with the solution. So, in comparing the given equation which is a square b square into x square minus 4 b raised to the power 4 minus 3 times of a raised to the power 4 into x minus 12 times of a square b square is equal to 0. Let this be equation number 1 and on comparing this with the general form of the quadratic equation we find here that p is equal to a square b square q is equal to minus 4 b raised to the power 4 minus 3 times of a raised to the power 4 and r is equal to minus 12 a square into b square. Now, first let us find the value of d which is given by q square minus 4 times of p into r. So, we have minus of 4 times of b raised to the power 4 minus 3 times of a raised to the power 4 whole square minus 4 times of p s a square into b square and r is minus 12 a square into b square this is for the equal to 4 times of b raised to the power 4 minus 3 times of a raised to the power 4 whole square plus 48 a raised to the power 4 into b raised to the power 4. This is for the equal to 4 times of b raised to the power 4 whole square plus 3 times of a raised to the power 4 whole square plus 24, sorry, here we have minus, since the formula to calculate x minus y whole square is x square plus y square minus 2 times of x into y. So, here we have 2 times of 4, b raised to the power 4 into 3 times of a raised to the power 4 plus 48 a raised to the power 4 into b raised to the power 4. Now, this one simplifying comes equal to 24 a raised to the power 4 into b raised to the power 4. And I'm simplifying these two, we have 4 times of b raised to the power 4 whole square plus 3 times of a raised to the power 4 whole square plus 24 a raised to the power 4 into b raised to the power 4. And this is further equal to 4 b raised to the power 4 plus 3 times of a raised to the power 4 whole square. So, this is the value of t. Therefore x which is equal to minus q plus minus root over d divided by 2 times of p is equal to minus of q is just minus 4b raised to the power 4 minus 3 times of a raised to the power 4 plus minus root over d gives 4b raised to the power 4 plus 3 times of a raised to the power 4. Since I am taking a square root on both the sides here we have the value of root d is equal to 4b raised to the power 4 plus 3 times of a raised to the power 4 is all divided by 2 times of p and p is a square into b square. So this is further equal to 4 times of b raised to the power 4 minus 3 times of a raised to the power 4 plus minus 4 times of b raised to the power 4 plus 3 times of a raised to the power 4 whole divided by 2 times of a square b square and this is further equal to on taking the plus sign first we have 8b raised to the power 4 divided by 2a square into b square or on taking the minus sign we have minus 6a raised to the power 4 divided by 2 times of a square into b square which is further equal to 2 4s are 8 cancelling b square by square this as it is. So we have 4b square divided by a square or from here we have on simplifying 3a square cancelling with a square so we have minus 3a square divided by b square thus on solving we get the values of x as 4b square divided by a square and minus 3a square divided by b square. So this completes the session by intake