2x^2=90^2

Solution for 2x^2=90^2 equation:

2x^2=90^2

We move all terms to the left:

2x^2-(90^2)=0

We add all the numbers together, and all the variables

2x^2-8100=0

a = 2; b = 0; c = -8100;
Δ = b2-4ac
Δ = 02-4·2·(-8100)
Δ = 64800
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:

$\sqrt{\Delta}=\sqrt{64800}=\sqrt{32400*2}=\sqrt{32400}*\sqrt{2}=180\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180\sqrt{2}}{2*2}=\frac{0-180\sqrt{2}}{4}
=-\frac{180\sqrt{2}}{4}
=-45\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180\sqrt{2}}{2*2}=\frac{0+180\sqrt{2}}{4}
=\frac{180\sqrt{2}}{4}
=45\sqrt{2}
$