0=29.4-7.15t-4.9t^2

Solution for 0=29.4-7.15t-4.9t^2 equation:

0=29.4-7.15t-4.9t^2

We move all terms to the left:

0-(29.4-7.15t-4.9t^2)=0

We add all the numbers together, and all the variables

-(29.4-7.15t-4.9t^2)=0

We get rid of parentheses

4.9t^2+7.15t-29.4=0

a = 4.9; b = 7.15; c = -29.4;
Δ = b2-4ac
Δ = 7.152-4·4.9·(-29.4)
Δ = 627.3625
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{-(7.15)-\sqrt{627.3625}}{2*4.9}=\frac{-7.15-\sqrt{627.3625}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.15)+\sqrt{627.3625}}{2*4.9}=\frac{-7.15+\sqrt{627.3625}}{9.8}
$