2x2-9x-108=0

Solution for 2x2-9x-108=0 equation:

2x^2-9x-108=0

a = 2; b = -9; c = -108;
Δ = b2-4ac
Δ = -92-4·2·(-108)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{105}}{2*2}=\frac{9-3\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{105}}{2*2}=\frac{9+3\sqrt{105}}{4}
$