4x+4x(x-15)=500

Solution for 4x+4x(x-15)=500 equation:

4x+4x(x-15)=500

We move all terms to the left:

4x+4x(x-15)-(500)=0

We multiply parentheses

4x^2+4x-60x-500=0

We add all the numbers together, and all the variables

4x^2-56x-500=0

a = 4; b = -56; c = -500;
Δ = b2-4ac
Δ = -562-4·4·(-500)
Δ = 11136
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:

$\sqrt{\Delta}=\sqrt{11136}=\sqrt{64*174}=\sqrt{64}*\sqrt{174}=8\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{174}}{2*4}=\frac{56-8\sqrt{174}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{174}}{2*4}=\frac{56+8\sqrt{174}}{8}
$