2x(x-4)=x+6

Solution for 2x(x-4)=x+6 equation:

2x(x-4)=x+6

We move all terms to the left:

2x(x-4)-(x+6)=0

We multiply parentheses

2x^2-8x-(x+6)=0

We get rid of parentheses

2x^2-8x-x-6=0

We add all the numbers together, and all the variables

2x^2-9x-6=0

a = 2; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·2·(-6)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{129}}{2*2}=\frac{9-\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*2}=\frac{9+\sqrt{129}}{4}
$