0=4x^2+40x-75

Solution for 0=4x^2+40x-75 equation:

0=4x^2+40x-75

We move all terms to the left:

0-(4x^2+40x-75)=0

We add all the numbers together, and all the variables

-(4x^2+40x-75)=0

We get rid of parentheses

-4x^2-40x+75=0

a = -4; b = -40; c = +75;
Δ = b2-4ac
Δ = -402-4·(-4)·75
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{7}}{2*-4}=\frac{40-20\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{7}}{2*-4}=\frac{40+20\sqrt{7}}{-8}
$