40=2.5t+4.9t^2

Solution for 40=2.5t+4.9t^2 equation:

40=2.5t+4.9t^2

We move all terms to the left:

40-(2.5t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-2.5t+40=0

a = -4.9; b = -2.5; c = +40;
Δ = b2-4ac
Δ = -2.52-4·(-4.9)·40
Δ = 790.25
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{-(-2.5)-\sqrt{790.25}}{2*-4.9}=\frac{2.5-\sqrt{790.25}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{790.25}}{2*-4.9}=\frac{2.5+\sqrt{790.25}}{-9.8}
$