40=80t-16t^2

Solution for 40=80t-16t^2 equation:

40=80t-16t^2

We move all terms to the left:

40-(80t-16t^2)=0

We get rid of parentheses

16t^2-80t+40=0

a = 16; b = -80; c = +40;
Δ = b2-4ac
Δ = -802-4·16·40
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{15}}{2*16}=\frac{80-16\sqrt{15}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{15}}{2*16}=\frac{80+16\sqrt{15}}{32}
$