16x^2-108x-216=0

Solution for 16x^2-108x-216=0 equation:

16x^2-108x-216=0

a = 16; b = -108; c = -216;
Δ = b2-4ac
Δ = -1082-4·16·(-216)
Δ = 25488
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:

$\sqrt{\Delta}=\sqrt{25488}=\sqrt{144*177}=\sqrt{144}*\sqrt{177}=12\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-12\sqrt{177}}{2*16}=\frac{108-12\sqrt{177}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+12\sqrt{177}}{2*16}=\frac{108+12\sqrt{177}}{32}
$