5=3+30t-16t^2

Solution for 5=3+30t-16t^2 equation:

5=3+30t-16t^2

We move all terms to the left:

5-(3+30t-16t^2)=0

We get rid of parentheses

16t^2-30t-3+5=0

We add all the numbers together, and all the variables

16t^2-30t+2=0

a = 16; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·16·2
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{193}}{2*16}=\frac{30-2\sqrt{193}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{193}}{2*16}=\frac{30+2\sqrt{193}}{32}
$