240=x*x-8

Solution for 240=x*x-8 equation:

240=x*x-8

We move all terms to the left:

240-(x*x-8)=0

We get rid of parentheses

-x*x+8+240=0

We add all the numbers together, and all the variables

-x*x+248=0

Wy multiply elements

-1x^2+248=0

a = -1; b = 0; c = +248;
Δ = b2-4ac
Δ = 02-4·(-1)·248
Δ = 992
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:

$\sqrt{\Delta}=\sqrt{992}=\sqrt{16*62}=\sqrt{16}*\sqrt{62}=4\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{62}}{2*-1}=\frac{0-4\sqrt{62}}{-2}
=-\frac{4\sqrt{62}}{-2}
=-\frac{2\sqrt{62}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{62}}{2*-1}=\frac{0+4\sqrt{62}}{-2}
=\frac{4\sqrt{62}}{-2}
=\frac{2\sqrt{62}}{-1}
$