256x^2+81x^2=189

Solution for 256x^2+81x^2=189 equation:

256x^2+81x^2=189

We move all terms to the left:

256x^2+81x^2-(189)=0

We add all the numbers together, and all the variables

337x^2-189=0

a = 337; b = 0; c = -189;
Δ = b2-4ac
Δ = 02-4·337·(-189)
Δ = 254772
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:

$\sqrt{\Delta}=\sqrt{254772}=\sqrt{36*7077}=\sqrt{36}*\sqrt{7077}=6\sqrt{7077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7077}}{2*337}=\frac{0-6\sqrt{7077}}{674}
=-\frac{6\sqrt{7077}}{674}
=-\frac{3\sqrt{7077}}{337}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7077}}{2*337}=\frac{0+6\sqrt{7077}}{674}
=\frac{6\sqrt{7077}}{674}
=\frac{3\sqrt{7077}}{337}
$