(X-4)(3x+8)=180

Solution for (X-4)(3x+8)=180 equation:

(X-4)(3X+8)=180

We move all terms to the left:

(X-4)(3X+8)-(180)=0

We multiply parentheses ..

(+3X^2+8X-12X-32)-180=0

We get rid of parentheses

3X^2+8X-12X-32-180=0

We add all the numbers together, and all the variables

3X^2-4X-212=0

a = 3; b = -4; c = -212;
Δ = b2-4ac
Δ = -42-4·3·(-212)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16\sqrt{10}}{2*3}=\frac{4-16\sqrt{10}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16\sqrt{10}}{2*3}=\frac{4+16\sqrt{10}}{6}
$