-5t^2+15t=-100

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

-5t^2+15t=-100

We move all terms to the left:

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

We add all the numbers together, and all the variables

-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}
$