9x^2-128x-320=0

Solution for 9x^2-128x-320=0 equation:

9x^2-128x-320=0

a = 9; b = -128; c = -320;
Δ = b2-4ac
Δ = -1282-4·9·(-320)
Δ = 27904
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:

$\sqrt{\Delta}=\sqrt{27904}=\sqrt{256*109}=\sqrt{256}*\sqrt{109}=16\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-16\sqrt{109}}{2*9}=\frac{128-16\sqrt{109}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+16\sqrt{109}}{2*9}=\frac{128+16\sqrt{109}}{18}
$