-2t^2-36t-100=0

Solution for -2t^2-36t-100=0 equation:

-2t^2-36t-100=0

a = -2; b = -36; c = -100;
Δ = b2-4ac
Δ = -362-4·(-2)·(-100)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{31}}{2*-2}=\frac{36-4\sqrt{31}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{31}}{2*-2}=\frac{36+4\sqrt{31}}{-4}
$