(10x-10)(5x+10)=180

Solution for (10x-10)(5x+10)=180 equation:

(10x-10)(5x+10)=180

We move all terms to the left:

(10x-10)(5x+10)-(180)=0

We multiply parentheses ..

(+50x^2+100x-50x-100)-180=0

We get rid of parentheses

50x^2+100x-50x-100-180=0

We add all the numbers together, and all the variables

50x^2+50x-280=0

a = 50; b = 50; c = -280;
Δ = b2-4ac
Δ = 502-4·50·(-280)
Δ = 58500
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:

$\sqrt{\Delta}=\sqrt{58500}=\sqrt{900*65}=\sqrt{900}*\sqrt{65}=30\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30\sqrt{65}}{2*50}=\frac{-50-30\sqrt{65}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30\sqrt{65}}{2*50}=\frac{-50+30\sqrt{65}}{100}
$