2x^2+10=44-x^2

Solution for 2x^2+10=44-x^2 equation:

2x^2+10=44-x^2

We move all terms to the left:

2x^2+10-(44-x^2)=0

We get rid of parentheses

2x^2+x^2-44+10=0

We add all the numbers together, and all the variables

3x^2-34=0

a = 3; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·3·(-34)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{102}}{2*3}=\frac{0-2\sqrt{102}}{6}
=-\frac{2\sqrt{102}}{6}
=-\frac{\sqrt{102}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{102}}{2*3}=\frac{0+2\sqrt{102}}{6}
=\frac{2\sqrt{102}}{6}
=\frac{\sqrt{102}}{3}
$