34^2=2x^2

Solution for 34^2=2x^2 equation:

34^2=2x^2

We move all terms to the left:

34^2-(2x^2)=0

We add all the numbers together, and all the variables

-2x^2+1156=0

a = -2; b = 0; c = +1156;
Δ = b2-4ac
Δ = 02-4·(-2)·1156
Δ = 9248
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:

$\sqrt{\Delta}=\sqrt{9248}=\sqrt{4624*2}=\sqrt{4624}*\sqrt{2}=68\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-68\sqrt{2}}{2*-2}=\frac{0-68\sqrt{2}}{-4}
=-\frac{68\sqrt{2}}{-4}
=-\frac{17\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+68\sqrt{2}}{2*-2}=\frac{0+68\sqrt{2}}{-4}
=\frac{68\sqrt{2}}{-4}
=\frac{17\sqrt{2}}{-1}
$