(2x-10)(5x+15)=180

Solution for (2x-10)(5x+15)=180 equation:

(2x-10)(5x+15)=180

We move all terms to the left:

(2x-10)(5x+15)-(180)=0

We multiply parentheses ..

(+10x^2+30x-50x-150)-180=0

We get rid of parentheses

10x^2+30x-50x-150-180=0

We add all the numbers together, and all the variables

10x^2-20x-330=0

a = 10; b = -20; c = -330;
Δ = b2-4ac
Δ = -202-4·10·(-330)
Δ = 13600
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:

$\sqrt{\Delta}=\sqrt{13600}=\sqrt{400*34}=\sqrt{400}*\sqrt{34}=20\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{34}}{2*10}=\frac{20-20\sqrt{34}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{34}}{2*10}=\frac{20+20\sqrt{34}}{20}
$