x^2+(2x)^2=52

Solution for x^2+(2x)^2=52 equation:

x^2+(2x)^2=52

We move all terms to the left:

x^2+(2x)^2-(52)=0

We add all the numbers together, and all the variables

3x^2-52=0

a = 3; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·3·(-52)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*3}=\frac{0-4\sqrt{39}}{6}
=-\frac{4\sqrt{39}}{6}
=-\frac{2\sqrt{39}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*3}=\frac{0+4\sqrt{39}}{6}
=\frac{4\sqrt{39}}{6}
=\frac{2\sqrt{39}}{3}
$