(10x-20)(6x+8)=180

Solution for (10x-20)(6x+8)=180 equation:

(10x-20)(6x+8)=180

We move all terms to the left:

(10x-20)(6x+8)-(180)=0

We multiply parentheses ..

(+60x^2+80x-120x-160)-180=0

We get rid of parentheses

60x^2+80x-120x-160-180=0

We add all the numbers together, and all the variables

60x^2-40x-340=0

a = 60; b = -40; c = -340;
Δ = b2-4ac
Δ = -402-4·60·(-340)
Δ = 83200
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:

$\sqrt{\Delta}=\sqrt{83200}=\sqrt{6400*13}=\sqrt{6400}*\sqrt{13}=80\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-80\sqrt{13}}{2*60}=\frac{40-80\sqrt{13}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+80\sqrt{13}}{2*60}=\frac{40+80\sqrt{13}}{120}
$