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(12-2x)(12-2x)=135
We move all terms to the left:
(12-2x)(12-2x)-(135)=0
We add all the numbers together, and all the variables
(-2x+12)(-2x+12)-135=0
We multiply parentheses ..
(+4x^2-24x-24x+144)-135=0
We get rid of parentheses
4x^2-24x-24x+144-135=0
We add all the numbers together, and all the variables
4x^2-48x+9=0
a = 4; b = -48; c = +9;
Δ = b2-4ac
Δ = -482-4·4·9
Δ = 2160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{15}}{2*4}=\frac{48-12\sqrt{15}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{15}}{2*4}=\frac{48+12\sqrt{15}}{8} $
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