40=-4.9t^2+29.4t+1

Solution for 40=-4.9t^2+29.4t+1 equation:

40=-4.9t^2+29.4t+1

We move all terms to the left:

40-(-4.9t^2+29.4t+1)=0

We get rid of parentheses

4.9t^2-29.4t-1+40=0

We add all the numbers together, and all the variables

4.9t^2-29.4t+39=0

a = 4.9; b = -29.4; c = +39;
Δ = b2-4ac
Δ = -29.42-4·4.9·39
Δ = 99.96
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{-(-29.4)-\sqrt{99.96}}{2*4.9}=\frac{29.4-\sqrt{99.96}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29.4)+\sqrt{99.96}}{2*4.9}=\frac{29.4+\sqrt{99.96}}{9.8}
$