8=22t-5t^2

Solution for 8=22t-5t^2 equation:

8=22t-5t^2

We move all terms to the left:

8-(22t-5t^2)=0

We get rid of parentheses

5t^2-22t+8=0

a = 5; b = -22; c = +8;
Δ = b2-4ac
Δ = -222-4·5·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-18}{2*5}=\frac{4}{10}
=2/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+18}{2*5}=\frac{40}{10}
=4
$