30^2=2x^2

Solution for 30^2=2x^2 equation:

30^2=2x^2

We move all terms to the left:

30^2-(2x^2)=0

We add all the numbers together, and all the variables

-2x^2+900=0

a = -2; b = 0; c = +900;
Δ = b2-4ac
Δ = 02-4·(-2)·900
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*-2}=\frac{0-60\sqrt{2}}{-4}
=-\frac{60\sqrt{2}}{-4}
=-\frac{15\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*-2}=\frac{0+60\sqrt{2}}{-4}
=\frac{60\sqrt{2}}{-4}
=\frac{15\sqrt{2}}{-1}
$