x(x-8)=100

Solution for x(x-8)=100 equation:

x(x-8)=100

We move all terms to the left:

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

We multiply parentheses

x^2-8x-100=0

a = 1; b = -8; c = -100;
Δ = b2-4ac
Δ = -82-4·1·(-100)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{29}}{2*1}=\frac{8-4\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{29}}{2*1}=\frac{8+4\sqrt{29}}{2}
$