x-5+x(x-2)=5x+8

Solution for x-5+x(x-2)=5x+8 equation:

x-5+x(x-2)=5x+8

We move all terms to the left:

x-5+x(x-2)-(5x+8)=0

We multiply parentheses

x^2+x-2x-(5x+8)-5=0

We get rid of parentheses

x^2+x-2x-5x-8-5=0

We add all the numbers together, and all the variables

x^2-6x-13=0

a = 1; b = -6; c = -13;
Δ = b2-4ac
Δ = -62-4·1·(-13)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{22}}{2*1}=\frac{6-2\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{22}}{2*1}=\frac{6+2\sqrt{22}}{2}
$