(12-2x)(12-x)=54

Solution for (12-2x)(12-x)=54 equation:

(12-2x)(12-x)=54

We move all terms to the left:

(12-2x)(12-x)-(54)=0

We add all the numbers together, and all the variables

(-2x+12)(-1x+12)-54=0

We multiply parentheses ..

(+2x^2-24x-12x+144)-54=0

We get rid of parentheses

2x^2-24x-12x+144-54=0

We add all the numbers together, and all the variables

2x^2-36x+90=0

a = 2; b = -36; c = +90;
Δ = b2-4ac
Δ = -362-4·2·90
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24}{2*2}=\frac{12}{4}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24}{2*2}=\frac{60}{4}
=15
$