5=16t^2+45t+6

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

5=16t^2+45t+6

We move all terms to the left:

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

We get rid of parentheses

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