x^2+2x^2=34^2

Solution for x^2+2x^2=34^2 equation:

x^2+2x^2=34^2

We move all terms to the left:

x^2+2x^2-(34^2)=0

We add all the numbers together, and all the variables

3x^2-1156=0

a = 3; b = 0; c = -1156;
Δ = b2-4ac
Δ = 02-4·3·(-1156)
Δ = 13872
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:

$\sqrt{\Delta}=\sqrt{13872}=\sqrt{4624*3}=\sqrt{4624}*\sqrt{3}=68\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-68\sqrt{3}}{2*3}=\frac{0-68\sqrt{3}}{6}
=-\frac{68\sqrt{3}}{6}
=-\frac{34\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+68\sqrt{3}}{2*3}=\frac{0+68\sqrt{3}}{6}
=\frac{68\sqrt{3}}{6}
=\frac{34\sqrt{3}}{3}
$