75(t)=75-16t^2

Solution for 75(t)=75-16t^2 equation:

75(t)=75-16t^2

We move all terms to the left:

75(t)-(75-16t^2)=0

We get rid of parentheses

16t^2+75t-75=0

a = 16; b = 75; c = -75;
Δ = b2-4ac
Δ = 752-4·16·(-75)
Δ = 10425
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:

$\sqrt{\Delta}=\sqrt{10425}=\sqrt{25*417}=\sqrt{25}*\sqrt{417}=5\sqrt{417}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-5\sqrt{417}}{2*16}=\frac{-75-5\sqrt{417}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+5\sqrt{417}}{2*16}=\frac{-75+5\sqrt{417}}{32}
$