(4x+16)(5x-12)=180

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Solution for (4x+16)(5x-12)=180 equation:



(4x+16)(5x-12)=180
We move all terms to the left:
(4x+16)(5x-12)-(180)=0
We multiply parentheses ..
(+20x^2-48x+80x-192)-180=0
We get rid of parentheses
20x^2-48x+80x-192-180=0
We add all the numbers together, and all the variables
20x^2+32x-372=0
a = 20; b = 32; c = -372;
Δ = b2-4ac
Δ = 322-4·20·(-372)
Δ = 30784
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:
$\sqrt{\Delta}=\sqrt{30784}=\sqrt{64*481}=\sqrt{64}*\sqrt{481}=8\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{481}}{2*20}=\frac{-32-8\sqrt{481}}{40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{481}}{2*20}=\frac{-32+8\sqrt{481}}{40} $

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