 welcome friends so let us take us example and try to solve it now in this question it is given that or it is rather being asked that determine whether x equals to minus half and x equals to 2 by 3 our solution of the equation which equation 6x square minus x minus 2 equals 0 so if you see this is a quadratic equation we are doing quadratic equation so this is a quadratic equation and we have and here if you see this is nothing but a is equal to 6 b equals minus 1 and c is minus 2 right and a general form of a quadratic equation is ax square plus bx plus c this is just a recap this is not required for solving this this question now they're asking if x equals to minus half and x equals to 2 by 3 our solution what is meant by solution so if you plug in the values of x in the given equation both LHS must be equal to RHS so let us see so instead of x we are plugging in minus half so 6 so let us say this is x equals to minus half so it is 6 times minus half whole squared minus minus half minus 2 equals whatever we'll just check so basically if you see wherever there was an x I have deployed minus half wherever there was an x there is minus half now let's simplify so this is nothing but 6 into a minus half square will be 1 upon 4 and then minus minus half is plus half and minus 2 isn't it which is nothing but 3 by 2 so this is 2 times 3 2 times 2 so 3 by 2 plus half minus 2 which is nothing but 2 minus 2 which is 0 which is equal to RHS that means we can declare that x equals to minus half is a solution a solution to the given quadratic equation similarly when x is equal to let us say it is given what is the value of x x is next values 2 upon 3 so 2 upon 3 let's check so wherever let's check LHS LHS is left hand side left hand side 6 into now 2 upon 3 whole squared minus 2 upon 3 and then minus 2 which is equal to if you see this is nothing but 6 times 4 upon 9 minus 2 upon 3 minus 2 so if I cancel 3 3 twice 3 thrice now what is it so LCM will be definitely 3 and you take up in the numerator it will be 2 times 4 so this 2 times 4 is 8 minus 2 and then minus 6 is it which comes out to be 0 again which is equal to RHS that means that means x equals to 2 upon 3 is a solution solution to which equation to equation the given equation was 6x squared minus x minus 2 equals 0 right so 2 2 solutions could be established okay so what do we learn we learn that if you want to check whether a particular value is a given solution so what you need to do is plug in the value in instead of the in place of the variable and try to simplify if LHS matches with RHS then the given value is a solution to the given equation