(6x-20)(8x+12)=180

Solution for (6x-20)(8x+12)=180 equation:

(6x-20)(8x+12)=180

We move all terms to the left:

(6x-20)(8x+12)-(180)=0

We multiply parentheses ..

(+48x^2+72x-160x-240)-180=0

We get rid of parentheses

48x^2+72x-160x-240-180=0

We add all the numbers together, and all the variables

48x^2-88x-420=0

a = 48; b = -88; c = -420;
Δ = b2-4ac
Δ = -882-4·48·(-420)
Δ = 88384
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:

$\sqrt{\Delta}=\sqrt{88384}=\sqrt{64*1381}=\sqrt{64}*\sqrt{1381}=8\sqrt{1381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8\sqrt{1381}}{2*48}=\frac{88-8\sqrt{1381}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8\sqrt{1381}}{2*48}=\frac{88+8\sqrt{1381}}{96}
$