4x^2-40x=-88

Solution for 4x^2-40x=-88 equation:

4x^2-40x=-88

We move all terms to the left:

4x^2-40x-(-88)=0

We add all the numbers together, and all the variables

4x^2-40x+88=0

a = 4; b = -40; c = +88;
Δ = b2-4ac
Δ = -402-4·4·88
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{3}}{2*4}=\frac{40-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{3}}{2*4}=\frac{40+8\sqrt{3}}{8}
$