324=x^2+64

Solution for 324=x^2+64 equation:

324=x^2+64

We move all terms to the left:

324-(x^2+64)=0

We get rid of parentheses

-x^2-64+324=0

We add all the numbers together, and all the variables

-1x^2+260=0

a = -1; b = 0; c = +260;
Δ = b2-4ac
Δ = 02-4·(-1)·260
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{65}}{2*-1}=\frac{0-4\sqrt{65}}{-2}
=-\frac{4\sqrt{65}}{-2}
=-\frac{2\sqrt{65}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{65}}{2*-1}=\frac{0+4\sqrt{65}}{-2}
=\frac{4\sqrt{65}}{-2}
=\frac{2\sqrt{65}}{-1}
$