256+x^2+81x^2=2500

Solution for 256+x^2+81x^2=2500 equation:

256+x^2+81x^2=2500

We move all terms to the left:

256+x^2+81x^2-(2500)=0

We add all the numbers together, and all the variables

82x^2-2244=0

a = 82; b = 0; c = -2244;
Δ = b2-4ac
Δ = 02-4·82·(-2244)
Δ = 736032
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:

$\sqrt{\Delta}=\sqrt{736032}=\sqrt{16*46002}=\sqrt{16}*\sqrt{46002}=4\sqrt{46002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46002}}{2*82}=\frac{0-4\sqrt{46002}}{164}
=-\frac{4\sqrt{46002}}{164}
=-\frac{\sqrt{46002}}{41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46002}}{2*82}=\frac{0+4\sqrt{46002}}{164}
=\frac{4\sqrt{46002}}{164}
=\frac{\sqrt{46002}}{41}
$