27x^2-39x-288=0

Solution for 27x^2-39x-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}
$