2x^2=330^2

Solution for 2x^2=330^2 equation:

2x^2=330^2

We move all terms to the left:

2x^2-(330^2)=0

We add all the numbers together, and all the variables

2x^2-108900=0

a = 2; b = 0; c = -108900;
Δ = b2-4ac
Δ = 02-4·2·(-108900)
Δ = 871200
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:

$\sqrt{\Delta}=\sqrt{871200}=\sqrt{435600*2}=\sqrt{435600}*\sqrt{2}=660\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-660\sqrt{2}}{2*2}=\frac{0-660\sqrt{2}}{4}
=-\frac{660\sqrt{2}}{4}
=-165\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+660\sqrt{2}}{2*2}=\frac{0+660\sqrt{2}}{4}
=\frac{660\sqrt{2}}{4}
=165\sqrt{2}
$