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(2x-12)(x-12)=54
We move all terms to the left:
(2x-12)(x-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 $
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