-100=15t-5t^2

Solution for -100=15t-5t^2 equation:

-100=15t-5t^2

We move all terms to the left:

-100-(15t-5t^2)=0

We get rid of parentheses

5t^2-15t-100=0

a = 5; b = -15; c = -100;
Δ = b2-4ac
Δ = -152-4·5·(-100)
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{89}}{2*5}=\frac{15-5\sqrt{89}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{89}}{2*5}=\frac{15+5\sqrt{89}}{10}
$