0=5t^2-5t-100

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

0=5t^2-5t-100

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -5; b = 5; c = +100;
Δ = b2-4ac
Δ = 52-4·(-5)·100
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-45}{2*-5}=\frac{-50}{-10}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+45}{2*-5}=\frac{40}{-10}
=-4
$