0=-5t^2+100t-10

Solution for 0=-5t^2+100t-10 equation:

0=-5t^2+100t-10

We move all terms to the left:

0-(-5t^2+100t-10)=0

We add all the numbers together, and all the variables

-(-5t^2+100t-10)=0

We get rid of parentheses

5t^2-100t+10=0

a = 5; b = -100; c = +10;
Δ = b2-4ac
Δ = -1002-4·5·10
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-70\sqrt{2}}{2*5}=\frac{100-70\sqrt{2}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+70\sqrt{2}}{2*5}=\frac{100+70\sqrt{2}}{10}
$