51=2x^2

Solution for 51=2x^2 equation:

51=2x^2

We move all terms to the left:

51-(2x^2)=0

a = -2; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-2)·51
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{102}}{2*-2}=\frac{0-2\sqrt{102}}{-4}
=-\frac{2\sqrt{102}}{-4}
=-\frac{\sqrt{102}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{102}}{2*-2}=\frac{0+2\sqrt{102}}{-4}
=\frac{2\sqrt{102}}{-4}
=\frac{\sqrt{102}}{-2}
$