0=2+70.71t-5t^2

Solution for 0=2+70.71t-5t^2 equation:

0=2+70.71t-5t^2

We move all terms to the left:

0-(2+70.71t-5t^2)=0

We add all the numbers together, and all the variables

-(2+70.71t-5t^2)=0

We get rid of parentheses

5t^2-70.71t-2=0

a = 5; b = -70.71; c = -2;
Δ = b2-4ac
Δ = -70.712-4·5·(-2)
Δ = 5039.9041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70.71)-\sqrt{5039.9041}}{2*5}=\frac{70.71-\sqrt{5039.9041}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70.71)+\sqrt{5039.9041}}{2*5}=\frac{70.71+\sqrt{5039.9041}}{10}
$