3x+9=2x^2-2

Solution for 3x+9=2x^2-2 equation:

3x+9=2x^2-2

We move all terms to the left:

3x+9-(2x^2-2)=0

We get rid of parentheses

-2x^2+3x+2+9=0

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +11;
Δ = b2-4ac
Δ = 32-4·(-2)·11
Δ = 97
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{-(3)-\sqrt{97}}{2*-2}=\frac{-3-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{97}}{2*-2}=\frac{-3+\sqrt{97}}{-4}
$