-20=-4t-5t^2

Solution for -20=-4t-5t^2 equation:

-20=-4t-5t^2

We move all terms to the left:

-20-(-4t-5t^2)=0

We get rid of parentheses

5t^2+4t-20=0

a = 5; b = 4; c = -20;
Δ = b2-4ac
Δ = 42-4·5·(-20)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{26}}{2*5}=\frac{-4-4\sqrt{26}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{26}}{2*5}=\frac{-4+4\sqrt{26}}{10}
$