4x^2=338

Solution for 4x^2=338 equation:

4x^2=338

We move all terms to the left:

4x^2-(338)=0

a = 4; b = 0; c = -338;
Δ = b2-4ac
Δ = 02-4·4·(-338)
Δ = 5408
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:

$\sqrt{\Delta}=\sqrt{5408}=\sqrt{2704*2}=\sqrt{2704}*\sqrt{2}=52\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{2}}{2*4}=\frac{0-52\sqrt{2}}{8}
=-\frac{52\sqrt{2}}{8}
=-\frac{13\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{2}}{2*4}=\frac{0+52\sqrt{2}}{8}
=\frac{52\sqrt{2}}{8}
=\frac{13\sqrt{2}}{2}
$