x^2+2(2x)^2=900

Solution for x^2+2(2x)^2=900 equation:

x^2+2(2x)^2=900

We move all terms to the left:

x^2+2(2x)^2-(900)=0

We add all the numbers together, and all the variables

23x^2-900=0

a = 23; b = 0; c = -900;
Δ = b2-4ac
Δ = 02-4·23·(-900)
Δ = 82800
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:

$\sqrt{\Delta}=\sqrt{82800}=\sqrt{3600*23}=\sqrt{3600}*\sqrt{23}=60\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{23}}{2*23}=\frac{0-60\sqrt{23}}{46}
=-\frac{60\sqrt{23}}{46}
=-\frac{30\sqrt{23}}{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{23}}{2*23}=\frac{0+60\sqrt{23}}{46}
=\frac{60\sqrt{23}}{46}
=\frac{30\sqrt{23}}{23}
$