X(x-6)=2x-8

Solution for X(x-6)=2x-8 equation:

X(X-6)=2X-8

We move all terms to the left:

X(X-6)-(2X-8)=0

We multiply parentheses

X^2-6X-(2X-8)=0

We get rid of parentheses

X^2-6X-2X+8=0

We add all the numbers together, and all the variables

X^2-8X+8=0

a = 1; b = -8; c = +8;
Δ = b2-4ac
Δ = -82-4·1·8
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{2}}{2*1}=\frac{8-4\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2}}{2*1}=\frac{8+4\sqrt{2}}{2}
$