6=-16t^2+45t+5

Solution for 6=-16t^2+45t+5 equation:

6=-16t^2+45t+5

We move all terms to the left:

6-(-16t^2+45t+5)=0

We get rid of parentheses

16t^2-45t-5+6=0

We add all the numbers together, and all the variables

16t^2-45t+1=0

a = 16; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·16·1
Δ = 1961
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{-(-45)-\sqrt{1961}}{2*16}=\frac{45-\sqrt{1961}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1961}}{2*16}=\frac{45+\sqrt{1961}}{32}
$