256x^2+81x^2=2500

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

256x^2+81x^2=2500

We move all terms to the left:

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

We add all the numbers together, and all the variables

337x^2-2500=0

a = 337; b = 0; c = -2500;
Δ = b2-4ac
Δ = 02-4·337·(-2500)
Δ = 3370000
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:

$\sqrt{\Delta}=\sqrt{3370000}=\sqrt{10000*337}=\sqrt{10000}*\sqrt{337}=100\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{337}}{2*337}=\frac{0-100\sqrt{337}}{674}
=-\frac{100\sqrt{337}}{674}
=-\frac{50\sqrt{337}}{337}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{337}}{2*337}=\frac{0+100\sqrt{337}}{674}
=\frac{100\sqrt{337}}{674}
=\frac{50\sqrt{337}}{337}
$