4x^2-9x-9^3=0

Solution for 4x^2-9x-9^3=0 equation:

4x^2-9x-9^3=0

We add all the numbers together, and all the variables

4x^2-9x-729=0

a = 4; b = -9; c = -729;
Δ = b2-4ac
Δ = -92-4·4·(-729)
Δ = 11745
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:

$\sqrt{\Delta}=\sqrt{11745}=\sqrt{81*145}=\sqrt{81}*\sqrt{145}=9\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{145}}{2*4}=\frac{9-9\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{145}}{2*4}=\frac{9+9\sqrt{145}}{8}
$