2x^2=2025

Solution for 2x^2=2025 equation:

2x^2=2025

We move all terms to the left:

2x^2-(2025)=0

a = 2; b = 0; c = -2025;
Δ = b2-4ac
Δ = 02-4·2·(-2025)
Δ = 16200
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:

$\sqrt{\Delta}=\sqrt{16200}=\sqrt{8100*2}=\sqrt{8100}*\sqrt{2}=90\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{2}}{2*2}=\frac{0-90\sqrt{2}}{4}
=-\frac{90\sqrt{2}}{4}
=-\frac{45\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{2}}{2*2}=\frac{0+90\sqrt{2}}{4}
=\frac{90\sqrt{2}}{4}
=\frac{45\sqrt{2}}{2}
$