2x^2-8=3x+9

Solution for 2x^2-8=3x+9 equation:

2x^2-8=3x+9

We move all terms to the left:

2x^2-8-(3x+9)=0

We get rid of parentheses

2x^2-3x-9-8=0

We add all the numbers together, and all the variables

2x^2-3x-17=0

a = 2; b = -3; c = -17;
Δ = b2-4ac
Δ = -32-4·2·(-17)
Δ = 145
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{145}}{2*2}=\frac{3-\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{145}}{2*2}=\frac{3+\sqrt{145}}{4}
$