5t=-16t^2+160t

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

5t=-16t^2+160t

We move all terms to the left:

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

We get rid of parentheses

16t^2-160t+5t=0

We add all the numbers together, and all the variables

16t^2-155t=0

a = 16; b = -155; c = 0;
Δ = b2-4ac
Δ = -1552-4·16·0
Δ = 24025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24025}=155$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-155)-155}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+155}{2*16}=\frac{310}{32}
=9+11/16
$