2x^2-27x-108=0

Solution for 2x^2-27x-108=0 equation:

2x^2-27x-108=0

a = 2; b = -27; c = -108;
Δ = b2-4ac
Δ = -272-4·2·(-108)
Δ = 1593
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:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{177}}{2*2}=\frac{27-3\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{177}}{2*2}=\frac{27+3\sqrt{177}}{4}
$