 Hi and welcome to the session. Let's work out the following question the question says solve for x a b x square Plus b square minus ac into x minus bc is equal to 0 So let us start with a solution to this question Now here we see that we have a b x square Plus b square minus ac into x Minus bc is equal to 0 now here if we compare this equation to the standard equation that is a x square plus Bx Plus c equals to 0 or let us say a dash x square Thus b dash x plus c dash equal to 0. So a dash is equal to a b b dash is equal to b square minus ac and C dash is equal to minus bc then we can find the determinant Sorry, it's discriminant d that is equal to b dash square minus 4 into a dash into c dash We simply put down the values here that is b square minus ac the whole square minus 4 into a b into minus bc That is equal to b square minus ac the whole square plus 4 into a b square c Therefore, we can say that x is equal to minus b plus minus square root of d divided by 2a or minus b dash to plus minus square root of d divided by 2a dash Now we can put down the values here and we have minus b square minus ac Plus minus square root of discriminant that is b square minus ac the whole square Plus 4 into a b square c divided by 2 into a dash a dash was equal to a b Now this is equal to minus b square minus ac plus minus square root of b square the whole square Plus ac the whole square minus 2 into b square into ac plus 4 a b square c and this divided by 2 a b Now this is equal to minus b square minus ac plus minus square root of b square the whole square plus 2 b square ac Plus ac the whole square divided by 2 a b and This is equal to minus b square minus ac plus minus square root of b square plus ac the whole square divided by 2 into a b This is equal to minus b square minus ac Plus minus now square root of b square plus ac the whole square is b square plus ac divided by 2a now We have two options that x can be equal to minus b square minus ac Plus b square plus ac divided by 2a or x is equal to minus b square minus ac minus b square plus ac divided by 2a Now this gives us x is equal to minus b square plus ac Plus b square plus ac divided by 2a This is equal to now minus b square gets cancelled with plus b square. We have 2 ac divided by 2a Now 2a gets cancelled with 2a now here we have b also So let us write down b here. We have 2 a b in the denominator here. Also. We have this 2 a b Here also we have b so we are left with c upon b Therefore x is equal to c upon b now. Let us solve this one here x is equal to minus b square plus ac minus b square minus ac divided by 2 a b This is equal to how plus ac gets cancelled with minus ac. We have minus 2 b square divided by plus 2 a b you see that 2 gets cancelled with 2 b gets cancelled with one of the b's in the numerator and we have minus b upon a So our answer to this question is that either x is equal to c upon b or x is equal to minus b by a So I hope that you understood the solution and enjoyed the session. Have a good day