256x^2+81x^2=750^2

Solution for 256x^2+81x^2=750^2 equation:

256x^2+81x^2=750^2

We move all terms to the left:

256x^2+81x^2-(750^2)=0

We add all the numbers together, and all the variables

337x^2-562500=0

a = 337; b = 0; c = -562500;
Δ = b2-4ac
Δ = 02-4·337·(-562500)
Δ = 758250000
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:

$\sqrt{\Delta}=\sqrt{758250000}=\sqrt{2250000*337}=\sqrt{2250000}*\sqrt{337}=1500\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1500\sqrt{337}}{2*337}=\frac{0-1500\sqrt{337}}{674}
=-\frac{1500\sqrt{337}}{674}
=-\frac{750\sqrt{337}}{337}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1500\sqrt{337}}{2*337}=\frac{0+1500\sqrt{337}}{674}
=\frac{1500\sqrt{337}}{674}
=\frac{750\sqrt{337}}{337}
$