X^2+(2x)^2=36

Solution for X^2+(2x)^2=36 equation:

X^2+(2X)^2=36

We move all terms to the left:

X^2+(2X)^2-(36)=0

We add all the numbers together, and all the variables

3X^2-36=0

a = 3; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·3·(-36)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*3}=\frac{0-12\sqrt{3}}{6}
=-\frac{12\sqrt{3}}{6}
=-2\sqrt{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*3}=\frac{0+12\sqrt{3}}{6}
=\frac{12\sqrt{3}}{6}
=2\sqrt{3}
$