2x^2+39x+108=0

Solution for 2x^2+39x+108=0 equation:

2x^2+39x+108=0

a = 2; b = 39; c = +108;
Δ = b2-4ac
Δ = 392-4·2·108
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{73}}{2*2}=\frac{-39-3\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{73}}{2*2}=\frac{-39+3\sqrt{73}}{4}
$