(5x-10)(3x+20)=180

Solution for (5x-10)(3x+20)=180 equation:

(5x-10)(3x+20)=180

We move all terms to the left:

(5x-10)(3x+20)-(180)=0

We multiply parentheses ..

(+15x^2+100x-30x-200)-180=0

We get rid of parentheses

15x^2+100x-30x-200-180=0

We add all the numbers together, and all the variables

15x^2+70x-380=0

a = 15; b = 70; c = -380;
Δ = b2-4ac
Δ = 702-4·15·(-380)
Δ = 27700
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:

$\sqrt{\Delta}=\sqrt{27700}=\sqrt{100*277}=\sqrt{100}*\sqrt{277}=10\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{277}}{2*15}=\frac{-70-10\sqrt{277}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{277}}{2*15}=\frac{-70+10\sqrt{277}}{30}
$