(3x)^2+(5x)^2=225

Solution for (3x)^2+(5x)^2=225 equation:

(3x)^2+(5x)^2=225

We move all terms to the left:

(3x)^2+(5x)^2-(225)=0

We add all the numbers together, and all the variables

8x^2-225=0

a = 8; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·8·(-225)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*8}=\frac{0-60\sqrt{2}}{16}
=-\frac{60\sqrt{2}}{16}
=-\frac{15\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*8}=\frac{0+60\sqrt{2}}{16}
=\frac{60\sqrt{2}}{16}
=\frac{15\sqrt{2}}{4}
$