-5t^2-100t+80=0

Solution for -5t^2-100t+80=0 equation:

-5t^2-100t+80=0

a = -5; b = -100; c = +80;
Δ = b2-4ac
Δ = -1002-4·(-5)·80
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{29}}{2*-5}=\frac{100-20\sqrt{29}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{29}}{2*-5}=\frac{100+20\sqrt{29}}{-10}
$