500(t)=-16t^2+175

Solution for 500(t)=-16t^2+175 equation:

500(t)=-16t^2+175

We move all terms to the left:

500(t)-(-16t^2+175)=0

We get rid of parentheses

16t^2+500t-175=0

a = 16; b = 500; c = -175;
Δ = b2-4ac
Δ = 5002-4·16·(-175)
Δ = 261200
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:

$\sqrt{\Delta}=\sqrt{261200}=\sqrt{400*653}=\sqrt{400}*\sqrt{653}=20\sqrt{653}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-20\sqrt{653}}{2*16}=\frac{-500-20\sqrt{653}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+20\sqrt{653}}{2*16}=\frac{-500+20\sqrt{653}}{32}
$