(2x-10)(2x+50)=360

Solution for (2x-10)(2x+50)=360 equation:

(2x-10)(2x+50)=360

We move all terms to the left:

(2x-10)(2x+50)-(360)=0

We multiply parentheses ..

(+4x^2+100x-20x-500)-360=0

We get rid of parentheses

4x^2+100x-20x-500-360=0

We add all the numbers together, and all the variables

4x^2+80x-860=0

a = 4; b = 80; c = -860;
Δ = b2-4ac
Δ = 802-4·4·(-860)
Δ = 20160
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:

$\sqrt{\Delta}=\sqrt{20160}=\sqrt{576*35}=\sqrt{576}*\sqrt{35}=24\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-24\sqrt{35}}{2*4}=\frac{-80-24\sqrt{35}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+24\sqrt{35}}{2*4}=\frac{-80+24\sqrt{35}}{8}
$