0=2x^2-53

Solution for 0=2x^2-53 equation:

0=2x^2-53

We move all terms to the left:

0-(2x^2-53)=0

We add all the numbers together, and all the variables

-(2x^2-53)=0

We get rid of parentheses

-2x^2+53=0

a = -2; b = 0; c = +53;
Δ = b2-4ac
Δ = 02-4·(-2)·53
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{106}}{2*-2}=\frac{0-2\sqrt{106}}{-4}
=-\frac{2\sqrt{106}}{-4}
=-\frac{\sqrt{106}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{106}}{2*-2}=\frac{0+2\sqrt{106}}{-4}
=\frac{2\sqrt{106}}{-4}
=\frac{\sqrt{106}}{-2}
$