(5x-10)(2x+50)=180

Solution for (5x-10)(2x+50)=180 equation:

(5x-10)(2x+50)=180

We move all terms to the left:

(5x-10)(2x+50)-(180)=0

We multiply parentheses ..

(+10x^2+250x-20x-500)-180=0

We get rid of parentheses

10x^2+250x-20x-500-180=0

We add all the numbers together, and all the variables

10x^2+230x-680=0

a = 10; b = 230; c = -680;
Δ = b2-4ac
Δ = 2302-4·10·(-680)
Δ = 80100
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:

$\sqrt{\Delta}=\sqrt{80100}=\sqrt{900*89}=\sqrt{900}*\sqrt{89}=30\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(230)-30\sqrt{89}}{2*10}=\frac{-230-30\sqrt{89}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(230)+30\sqrt{89}}{2*10}=\frac{-230+30\sqrt{89}}{20}
$