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(8x-4)(6x-12)=180
We move all terms to the left:
(8x-4)(6x-12)-(180)=0
We multiply parentheses ..
(+48x^2-96x-24x+48)-180=0
We get rid of parentheses
48x^2-96x-24x+48-180=0
We add all the numbers together, and all the variables
48x^2-120x-132=0
a = 48; b = -120; c = -132;
Δ = b2-4ac
Δ = -1202-4·48·(-132)
Δ = 39744
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39744}=\sqrt{576*69}=\sqrt{576}*\sqrt{69}=24\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{69}}{2*48}=\frac{120-24\sqrt{69}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{69}}{2*48}=\frac{120+24\sqrt{69}}{96} $
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