0=40+30.1t-4.9t^2

Solution for 0=40+30.1t-4.9t^2 equation:

0=40+30.1t-4.9t^2

We move all terms to the left:

0-(40+30.1t-4.9t^2)=0

We add all the numbers together, and all the variables

-(40+30.1t-4.9t^2)=0

We get rid of parentheses

4.9t^2-30.1t-40=0

a = 4.9; b = -30.1; c = -40;
Δ = b2-4ac
Δ = -30.12-4·4.9·(-40)
Δ = 1690.01
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{-(-30.1)-\sqrt{1690.01}}{2*4.9}=\frac{30.1-\sqrt{1690.01}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30.1)+\sqrt{1690.01}}{2*4.9}=\frac{30.1+\sqrt{1690.01}}{9.8}
$