(11x+8)(12x-4)=180

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Solution for (11x+8)(12x-4)=180 equation:



(11x+8)(12x-4)=180
We move all terms to the left:
(11x+8)(12x-4)-(180)=0
We multiply parentheses ..
(+132x^2-44x+96x-32)-180=0
We get rid of parentheses
132x^2-44x+96x-32-180=0
We add all the numbers together, and all the variables
132x^2+52x-212=0
a = 132; b = 52; c = -212;
Δ = b2-4ac
Δ = 522-4·132·(-212)
Δ = 114640
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:
$\sqrt{\Delta}=\sqrt{114640}=\sqrt{16*7165}=\sqrt{16}*\sqrt{7165}=4\sqrt{7165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{7165}}{2*132}=\frac{-52-4\sqrt{7165}}{264} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{7165}}{2*132}=\frac{-52+4\sqrt{7165}}{264} $

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