9^2+2x=x^2-5

Solution for 9^2+2x=x^2-5 equation:

9^2+2x=x^2-5

We move all terms to the left:

9^2+2x-(x^2-5)=0

We add all the numbers together, and all the variables

2x-(x^2-5)+81=0

We get rid of parentheses

-x^2+2x+5+81=0

We add all the numbers together, and all the variables

-1x^2+2x+86=0

a = -1; b = 2; c = +86;
Δ = b2-4ac
Δ = 22-4·(-1)·86
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{87}}{2*-1}=\frac{-2-2\sqrt{87}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{87}}{2*-1}=\frac{-2+2\sqrt{87}}{-2}
$