x=3x^2+12-6x-24

Solution for x=3x^2+12-6x-24 equation:

x=3x^2+12-6x-24

We move all terms to the left:

x-(3x^2+12-6x-24)=0

We get rid of parentheses

-3x^2+x+6x-12+24=0

We add all the numbers together, and all the variables

-3x^2+7x+12=0

a = -3; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-3)·12
Δ = 193
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{193}}{2*-3}=\frac{-7-\sqrt{193}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{193}}{2*-3}=\frac{-7+\sqrt{193}}{-6}
$