-27x2+39x+288=0

Solution for -27x2+39x+288=0 equation:

-27x^2+39x+288=0

a = -27; b = 39; c = +288;
Δ = b2-4ac
Δ = 392-4·(-27)·288
Δ = 32625
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:

$\sqrt{\Delta}=\sqrt{32625}=\sqrt{225*145}=\sqrt{225}*\sqrt{145}=15\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-15\sqrt{145}}{2*-27}=\frac{-39-15\sqrt{145}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+15\sqrt{145}}{2*-27}=\frac{-39+15\sqrt{145}}{-54}
$