2x+12=2x(x-6)

Solution for 2x+12=2x(x-6) equation:

2x+12=2x(x-6)

We move all terms to the left:

2x+12-(2x(x-6))=0


We calculate terms in parentheses: -(2x(x-6)), so:

2x(x-6)

We multiply parentheses

2x^2-12x

Back to the equation:

-(2x^2-12x)


We get rid of parentheses

-2x^2+2x+12x+12=0

We add all the numbers together, and all the variables

-2x^2+14x+12=0

a = -2; b = 14; c = +12;
Δ = b2-4ac
Δ = 142-4·(-2)·12
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{73}}{2*-2}=\frac{-14-2\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{73}}{2*-2}=\frac{-14+2\sqrt{73}}{-4}
$