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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+(2x-4)(x+6)=0

We multiply parentheses ..

(+2x^2+12x-4x-24)-1x=0

We get rid of parentheses

2x^2+12x-4x-1x-24=0

We add all the numbers together, and all the variables

2x^2+7x-24=0

a = 2; b = 7; c = -24;
Δ = b2-4ac
Δ = 72-4·2·(-24)
Δ = 241
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{-(7)-\sqrt{241}}{2*2}=\frac{-7-\sqrt{241}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{241}}{2*2}=\frac{-7+\sqrt{241}}{4}
$