X^2+(5x)^2=52^2

Solution for X^2+(5x)^2=52^2 equation:

X^2+(5X)^2=52^2

We move all terms to the left:

X^2+(5X)^2-(52^2)=0

We add all the numbers together, and all the variables

6X^2-2704=0

a = 6; b = 0; c = -2704;
Δ = b2-4ac
Δ = 02-4·6·(-2704)
Δ = 64896
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:

$\sqrt{\Delta}=\sqrt{64896}=\sqrt{10816*6}=\sqrt{10816}*\sqrt{6}=104\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104\sqrt{6}}{2*6}=\frac{0-104\sqrt{6}}{12}
=-\frac{104\sqrt{6}}{12}
=-\frac{26\sqrt{6}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104\sqrt{6}}{2*6}=\frac{0+104\sqrt{6}}{12}
=\frac{104\sqrt{6}}{12}
=\frac{26\sqrt{6}}{3}
$