75=(40)t-5t^2

Solution for 75=(40)t-5t^2 equation:

75=(40)t-5t^2

We move all terms to the left:

75-((40)t-5t^2)=0

We get rid of parentheses

5t^2-40t+75=0

a = 5; b = -40; c = +75;
Δ = b2-4ac
Δ = -402-4·5·75
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10}{2*5}=\frac{30}{10}
=3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10}{2*5}=\frac{50}{10}
=5
$