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(3x-6)(3x-6)=86
We move all terms to the left:
(3x-6)(3x-6)-(86)=0
We multiply parentheses ..
(+9x^2-18x-18x+36)-86=0
We get rid of parentheses
9x^2-18x-18x+36-86=0
We add all the numbers together, and all the variables
9x^2-36x-50=0
a = 9; b = -36; c = -50;
Δ = b2-4ac
Δ = -362-4·9·(-50)
Δ = 3096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{86}}{2*9}=\frac{36-6\sqrt{86}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{86}}{2*9}=\frac{36+6\sqrt{86}}{18} $
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