F(5)=-16t^2+160

Solution for F(5)=-16t^2+160 equation:

(5)=-16F^2+160

We move all terms to the left:

(5)-(-16F^2+160)=0

We get rid of parentheses

16F^2-160+5=0

We add all the numbers together, and all the variables

16F^2-155=0

a = 16; b = 0; c = -155;
Δ = b2-4ac
Δ = 02-4·16·(-155)
Δ = 9920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9920}=\sqrt{64*155}=\sqrt{64}*\sqrt{155}=8\sqrt{155}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{155}}{2*16}=\frac{0-8\sqrt{155}}{32}
=-\frac{8\sqrt{155}}{32}
=-\frac{\sqrt{155}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{155}}{2*16}=\frac{0+8\sqrt{155}}{32}
=\frac{8\sqrt{155}}{32}
=\frac{\sqrt{155}}{4}
$