84=-4t^2+40t

Solution for 84=-4t^2+40t equation:

84=-4t^2+40t

We move all terms to the left:

84-(-4t^2+40t)=0

We get rid of parentheses

4t^2-40t+84=0

a = 4; b = -40; c = +84;
Δ = b2-4ac
Δ = -402-4·4·84
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16}{2*4}=\frac{24}{8}
=3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16}{2*4}=\frac{56}{8}
=7
$