4x^2-20x-75=180

Solution for 4x^2-20x-75=180 equation:

4x^2-20x-75=180

We move all terms to the left:

4x^2-20x-75-(180)=0

We add all the numbers together, and all the variables

4x^2-20x-255=0

a = 4; b = -20; c = -255;
Δ = b2-4ac
Δ = -202-4·4·(-255)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{70}}{2*4}=\frac{20-8\sqrt{70}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{70}}{2*4}=\frac{20+8\sqrt{70}}{8}
$