16x^2-21x-108=0

Solution for 16x^2-21x-108=0 equation:

16x^2-21x-108=0

a = 16; b = -21; c = -108;
Δ = b2-4ac
Δ = -212-4·16·(-108)
Δ = 7353
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:

$\sqrt{\Delta}=\sqrt{7353}=\sqrt{9*817}=\sqrt{9}*\sqrt{817}=3\sqrt{817}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{817}}{2*16}=\frac{21-3\sqrt{817}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{817}}{2*16}=\frac{21+3\sqrt{817}}{32}
$