-16t^2-27t+118=0

Solution for -16t^2-27t+118=0 equation:

-16t^2-27t+118=0

a = -16; b = -27; c = +118;
Δ = b2-4ac
Δ = -272-4·(-16)·118
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-91}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+91}{2*-16}=\frac{118}{-32}
=-3+11/16
$