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(6x-6)(6x-6)=180
We move all terms to the left:
(6x-6)(6x-6)-(180)=0
We multiply parentheses ..
(+36x^2-36x-36x+36)-180=0
We get rid of parentheses
36x^2-36x-36x+36-180=0
We add all the numbers together, and all the variables
36x^2-72x-144=0
a = 36; b = -72; c = -144;
Δ = b2-4ac
Δ = -722-4·36·(-144)
Δ = 25920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25920}=\sqrt{5184*5}=\sqrt{5184}*\sqrt{5}=72\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72\sqrt{5}}{2*36}=\frac{72-72\sqrt{5}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72\sqrt{5}}{2*36}=\frac{72+72\sqrt{5}}{72} $
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