(x)^2+(2x)^2=45^2

Solution for (x)^2+(2x)^2=45^2 equation:

(x)^2+(2x)^2=45^2

We move all terms to the left:

(x)^2+(2x)^2-(45^2)=0

We add all the numbers together, and all the variables

3x^2-2025=0

a = 3; b = 0; c = -2025;
Δ = b2-4ac
Δ = 02-4·3·(-2025)
Δ = 24300
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:

$\sqrt{\Delta}=\sqrt{24300}=\sqrt{8100*3}=\sqrt{8100}*\sqrt{3}=90\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{3}}{2*3}=\frac{0-90\sqrt{3}}{6}
=-\frac{90\sqrt{3}}{6}
=-15\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{3}}{2*3}=\frac{0+90\sqrt{3}}{6}
=\frac{90\sqrt{3}}{6}
=15\sqrt{3}
$