96-(12-x)(8-x)=18

Solution for 96-(12-x)(8-x)=18 equation:

96-(12-x)(8-x)=18

We move all terms to the left:

96-(12-x)(8-x)-(18)=0

We add all the numbers together, and all the variables

-(-1x+12)(-1x+8)+96-18=0

We add all the numbers together, and all the variables

-(-1x+12)(-1x+8)+78=0

We multiply parentheses ..

-(+x^2-8x-12x+96)+78=0

We get rid of parentheses

-x^2+8x+12x-96+78=0

We add all the numbers together, and all the variables

-1x^2+20x-18=0

a = -1; b = 20; c = -18;
Δ = b2-4ac
Δ = 202-4·(-1)·(-18)
Δ = 328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{82}}{2*-1}=\frac{-20-2\sqrt{82}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{82}}{2*-1}=\frac{-20+2\sqrt{82}}{-2}
$