75=-16t^2+80t+4

Solution for 75=-16t^2+80t+4 equation:

75=-16t^2+80t+4

We move all terms to the left:

75-(-16t^2+80t+4)=0

We get rid of parentheses

16t^2-80t-4+75=0

We add all the numbers together, and all the variables

16t^2-80t+71=0

a = 16; b = -80; c = +71;
Δ = b2-4ac
Δ = -802-4·16·71
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{29}}{2*16}=\frac{80-8\sqrt{29}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{29}}{2*16}=\frac{80+8\sqrt{29}}{32}
$