x(x-11)=8

Solution for x(x-11)=8 equation:

x(x-11)=8

We move all terms to the left:

x(x-11)-(8)=0

We multiply parentheses

x^2-11x-8=0

a = 1; b = -11; c = -8;
Δ = b2-4ac
Δ = -112-4·1·(-8)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{17}}{2*1}=\frac{11-3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{17}}{2*1}=\frac{11+3\sqrt{17}}{2}
$