0=40t-5t^2+100

Solution for 0=40t-5t^2+100 equation:

0=40t-5t^2+100

We move all terms to the left:

0-(40t-5t^2+100)=0

We add all the numbers together, and all the variables

-(40t-5t^2+100)=0

We get rid of parentheses

5t^2-40t-100=0

a = 5; b = -40; c = -100;
Δ = b2-4ac
Δ = -402-4·5·(-100)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-60}{2*5}=\frac{-20}{10}
=-2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+60}{2*5}=\frac{100}{10}
=10
$