(3x)^2+x^2=15^2

Solution for (3x)^2+x^2=15^2 equation:

(3x)^2+x^2=15^2

We move all terms to the left:

(3x)^2+x^2-(15^2)=0

We add all the numbers together, and all the variables

4x^2-225=0

a = 4; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·4·(-225)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*4}=\frac{-60}{8}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*4}=\frac{60}{8}
=7+1/2
$