(3x)^2+x^2=360

Solution for (3x)^2+x^2=360 equation:

(3x)^2+x^2=360

We move all terms to the left:

(3x)^2+x^2-(360)=0

We add all the numbers together, and all the variables

4x^2-360=0

a = 4; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·4·(-360)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{10}}{2*4}=\frac{0-24\sqrt{10}}{8}
=-\frac{24\sqrt{10}}{8}
=-3\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{10}}{2*4}=\frac{0+24\sqrt{10}}{8}
=\frac{24\sqrt{10}}{8}
=3\sqrt{10}
$