x^2=578

Solution for x^2=578 equation:

x^2=578

We move all terms to the left:

x^2-(578)=0

a = 1; b = 0; c = -578;
Δ = b2-4ac
Δ = 02-4·1·(-578)
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{2}}{2*1}=\frac{0-34\sqrt{2}}{2}
=-\frac{34\sqrt{2}}{2}
=-17\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{2}}{2*1}=\frac{0+34\sqrt{2}}{2}
=\frac{34\sqrt{2}}{2}
=17\sqrt{2}
$