2x^2-2=-6x+9

Solution for 2x^2-2=-6x+9 equation:

2x^2-2=-6x+9

We move all terms to the left:

2x^2-2-(-6x+9)=0

We get rid of parentheses

2x^2+6x-9-2=0

We add all the numbers together, and all the variables

2x^2+6x-11=0

a = 2; b = 6; c = -11;
Δ = b2-4ac
Δ = 62-4·2·(-11)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{31}}{2*2}=\frac{-6-2\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{31}}{2*2}=\frac{-6+2\sqrt{31}}{4}
$