256x^2+9x-81=0

Solution for 256x^2+9x-81=0 equation:

256x^2+9x-81=0

a = 256; b = 9; c = -81;
Δ = b2-4ac
Δ = 92-4·256·(-81)
Δ = 83025
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:

$\sqrt{\Delta}=\sqrt{83025}=\sqrt{2025*41}=\sqrt{2025}*\sqrt{41}=45\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-45\sqrt{41}}{2*256}=\frac{-9-45\sqrt{41}}{512}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+45\sqrt{41}}{2*256}=\frac{-9+45\sqrt{41}}{512}
$