-12+4x^2+2x-9x-24-x^2=2x^2-2

Solution for -12+4x^2+2x-9x-24-x^2=2x^2-2 equation:

-12+4x^2+2x-9x-24-x^2=2x^2-2

We move all terms to the left:

-12+4x^2+2x-9x-24-x^2-(2x^2-2)=0

We add all the numbers together, and all the variables

3x^2-7x-(2x^2-2)-36=0

We get rid of parentheses

3x^2-2x^2-7x+2-36=0

We add all the numbers together, and all the variables

x^2-7x-34=0

a = 1; b = -7; c = -34;
Δ = b2-4ac
Δ = -72-4·1·(-34)
Δ = 185
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{185}}{2*1}=\frac{7-\sqrt{185}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{185}}{2*1}=\frac{7+\sqrt{185}}{2}
$