-40=100t-4.9t^2

Solution for -40=100t-4.9t^2 equation:

-40=100t-4.9t^2

We move all terms to the left:

-40-(100t-4.9t^2)=0

We get rid of parentheses

4.9t^2-100t-40=0

a = 4.9; b = -100; c = -40;
Δ = b2-4ac
Δ = -1002-4·4.9·(-40)
Δ = 10784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10784}=\sqrt{16*674}=\sqrt{16}*\sqrt{674}=4\sqrt{674}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{674}}{2*4.9}=\frac{100-4\sqrt{674}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{674}}{2*4.9}=\frac{100+4\sqrt{674}}{9.8}
$