x*x+2=510

Solution for x*x+2=510 equation:

x*x+2=510

We move all terms to the left:

x*x+2-(510)=0

We add all the numbers together, and all the variables

x*x-508=0

Wy multiply elements

x^2-508=0

a = 1; b = 0; c = -508;
Δ = b2-4ac
Δ = 02-4·1·(-508)
Δ = 2032
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:

$\sqrt{\Delta}=\sqrt{2032}=\sqrt{16*127}=\sqrt{16}*\sqrt{127}=4\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{127}}{2*1}=\frac{0-4\sqrt{127}}{2}
=-\frac{4\sqrt{127}}{2}
=-2\sqrt{127}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{127}}{2*1}=\frac{0+4\sqrt{127}}{2}
=\frac{4\sqrt{127}}{2}
=2\sqrt{127}
$