X(x-5)=x+2x+6

Solution for X(x-5)=x+2x+6 equation:

X(X-5)=X+2X+6

We move all terms to the left:

X(X-5)-(X+2X+6)=0

We add all the numbers together, and all the variables

X(X-5)-(3X+6)=0

We multiply parentheses

X^2-5X-(3X+6)=0

We get rid of parentheses

X^2-5X-3X-6=0

We add all the numbers together, and all the variables

X^2-8X-6=0

a = 1; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·1·(-6)
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{-(-8)-2\sqrt{22}}{2*1}=\frac{8-2\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*1}=\frac{8+2\sqrt{22}}{2}
$