0=2x^2-312

Solution for 0=2x^2-312 equation:

0=2x^2-312

We move all terms to the left:

0-(2x^2-312)=0

We add all the numbers together, and all the variables

-(2x^2-312)=0

We get rid of parentheses

-2x^2+312=0

a = -2; b = 0; c = +312;
Δ = b2-4ac
Δ = 02-4·(-2)·312
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{39}}{2*-2}=\frac{0-8\sqrt{39}}{-4}
=-\frac{8\sqrt{39}}{-4}
=-\frac{2\sqrt{39}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{39}}{2*-2}=\frac{0+8\sqrt{39}}{-4}
=\frac{8\sqrt{39}}{-4}
=\frac{2\sqrt{39}}{-1}
$