75=-5t^2+80t

Solution for 75=-5t^2+80t equation:

75=-5t^2+80t

We move all terms to the left:

75-(-5t^2+80t)=0

We get rid of parentheses

5t^2-80t+75=0

a = 5; b = -80; c = +75;
Δ = b2-4ac
Δ = -802-4·5·75
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-70}{2*5}=\frac{10}{10}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+70}{2*5}=\frac{150}{10}
=15
$