-3x(x-4)+x=2x-12

Solution for -3x(x-4)+x=2x-12 equation:

-3x(x-4)+x=2x-12

We move all terms to the left:

-3x(x-4)+x-(2x-12)=0

We add all the numbers together, and all the variables

x-3x(x-4)-(2x-12)=0

We multiply parentheses

-3x^2+x+12x-(2x-12)=0

We get rid of parentheses

-3x^2+x+12x-2x+12=0

We add all the numbers together, and all the variables

-3x^2+11x+12=0

a = -3; b = 11; c = +12;
Δ = b2-4ac
Δ = 112-4·(-3)·12
Δ = 265
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{-(11)-\sqrt{265}}{2*-3}=\frac{-11-\sqrt{265}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{265}}{2*-3}=\frac{-11+\sqrt{265}}{-6}
$