(3x+7)(4x-16)=180

Solution for (3x+7)(4x-16)=180 equation:

(3x+7)(4x-16)=180

We move all terms to the left:

(3x+7)(4x-16)-(180)=0

We multiply parentheses ..

(+12x^2-48x+28x-112)-180=0

We get rid of parentheses

12x^2-48x+28x-112-180=0

We add all the numbers together, and all the variables

12x^2-20x-292=0

a = 12; b = -20; c = -292;
Δ = b2-4ac
Δ = -202-4·12·(-292)
Δ = 14416
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:

$\sqrt{\Delta}=\sqrt{14416}=\sqrt{16*901}=\sqrt{16}*\sqrt{901}=4\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{901}}{2*12}=\frac{20-4\sqrt{901}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{901}}{2*12}=\frac{20+4\sqrt{901}}{24}
$