4x2+4x=500

Solution for 4x2+4x=500 equation:

4x^2+4x=500

We move all terms to the left:

4x^2+4x-(500)=0

a = 4; b = 4; c = -500;
Δ = b2-4ac
Δ = 42-4·4·(-500)
Δ = 8016
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:

$\sqrt{\Delta}=\sqrt{8016}=\sqrt{16*501}=\sqrt{16}*\sqrt{501}=4\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{501}}{2*4}=\frac{-4-4\sqrt{501}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{501}}{2*4}=\frac{-4+4\sqrt{501}}{8}
$