4x(x+8)=100

Solution for 4x(x+8)=100 equation:

4x(x+8)=100

We move all terms to the left:

4x(x+8)-(100)=0

We multiply parentheses

4x^2+32x-100=0

a = 4; b = 32; c = -100;
Δ = b2-4ac
Δ = 322-4·4·(-100)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{41}}{2*4}=\frac{-32-8\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{41}}{2*4}=\frac{-32+8\sqrt{41}}{8}
$