X^2+2(x)^2=450

Solution for X^2+2(x)^2=450 equation:

X^2+2(X)^2=450

We move all terms to the left:

X^2+2(X)^2-(450)=0

We add all the numbers together, and all the variables

3X^2-450=0

a = 3; b = 0; c = -450;
Δ = b2-4ac
Δ = 02-4·3·(-450)
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{6}}{2*3}=\frac{0-30\sqrt{6}}{6}
=-\frac{30\sqrt{6}}{6}
=-5\sqrt{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{6}}{2*3}=\frac{0+30\sqrt{6}}{6}
=\frac{30\sqrt{6}}{6}
=5\sqrt{6}
$