0=100+10t-2t^2

Solution for 0=100+10t-2t^2 equation:

0=100+10t-2t^2

We move all terms to the left:

0-(100+10t-2t^2)=0

We add all the numbers together, and all the variables

-(100+10t-2t^2)=0

We get rid of parentheses

2t^2-10t-100=0

a = 2; b = -10; c = -100;
Δ = b2-4ac
Δ = -102-4·2·(-100)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*2}=\frac{-20}{4}
=-5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*2}=\frac{40}{4}
=10
$