5(t)=-16t^2+5

Solution for 5(t)=-16t^2+5 equation:

5(t)=-16t^2+5

We move all terms to the left:

5(t)-(-16t^2+5)=0

We get rid of parentheses

16t^2+5t-5=0

a = 16; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·16·(-5)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{345}}{2*16}=\frac{-5-\sqrt{345}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{345}}{2*16}=\frac{-5+\sqrt{345}}{32}
$