256x^2+81x^2=11664

Solution for 256x^2+81x^2=11664 equation:

256x^2+81x^2=11664

We move all terms to the left:

256x^2+81x^2-(11664)=0

We add all the numbers together, and all the variables

337x^2-11664=0

a = 337; b = 0; c = -11664;
Δ = b2-4ac
Δ = 02-4·337·(-11664)
Δ = 15723072
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:

$\sqrt{\Delta}=\sqrt{15723072}=\sqrt{46656*337}=\sqrt{46656}*\sqrt{337}=216\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-216\sqrt{337}}{2*337}=\frac{0-216\sqrt{337}}{674}
=-\frac{216\sqrt{337}}{674}
=-\frac{108\sqrt{337}}{337}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+216\sqrt{337}}{2*337}=\frac{0+216\sqrt{337}}{674}
=\frac{216\sqrt{337}}{674}
=\frac{108\sqrt{337}}{337}
$