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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+6x-12=0

a = 4; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·4·(-12)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*4}=\frac{-6-2\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*4}=\frac{-6+2\sqrt{57}}{8}
$