5=5+9t-16t^2

Solution for 5=5+9t-16t^2 equation:

5=5+9t-16t^2

We move all terms to the left:

5-(5+9t-16t^2)=0

We get rid of parentheses

16t^2-9t-5+5=0

We add all the numbers together, and all the variables

16t^2-9t=0

a = 16; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·16·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*16}=\frac{18}{32}
=9/16
$