x^2+8=540

Solution for x^2+8=540 equation:

x^2+8=540

We move all terms to the left:

x^2+8-(540)=0

We add all the numbers together, and all the variables

x^2-532=0

a = 1; b = 0; c = -532;
Δ = b2-4ac
Δ = 02-4·1·(-532)
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{133}}{2*1}=\frac{0-4\sqrt{133}}{2}
=-\frac{4\sqrt{133}}{2}
=-2\sqrt{133}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{133}}{2*1}=\frac{0+4\sqrt{133}}{2}
=\frac{4\sqrt{133}}{2}
=2\sqrt{133}
$