2x+13=x2-2

Solution for 2x+13=x2-2 equation:

2x+13=x2-2

We move all terms to the left:

2x+13-(x2-2)=0

We add all the numbers together, and all the variables

-(+x^2-2)+2x+13=0

We get rid of parentheses

-x^2+2x+2+13=0

We add all the numbers together, and all the variables

-1x^2+2x+15=0

a = -1; b = 2; c = +15;
Δ = b2-4ac
Δ = 22-4·(-1)·15
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*-1}=\frac{6}{-2}
=-3
$