256x^2+81x^2=30.25

Solution for 256x^2+81x^2=30.25 equation:

256x^2+81x^2=30.25

We move all terms to the left:

256x^2+81x^2-(30.25)=0

We add all the numbers together, and all the variables

337x^2-30.25=0

a = 337; b = 0; c = -30.25;
Δ = b2-4ac
Δ = 02-4·337·(-30.25)
Δ = 40777
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:

$\sqrt{\Delta}=\sqrt{40777}=\sqrt{121*337}=\sqrt{121}*\sqrt{337}=11\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-11\sqrt{337}}{2*337}=\frac{0-11\sqrt{337}}{674}
=-\frac{11\sqrt{337}}{674}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+11\sqrt{337}}{2*337}=\frac{0+11\sqrt{337}}{674}
=\frac{11\sqrt{337}}{674}
$