45=-5t^2+80t+1

Solution for 45=-5t^2+80t+1 equation:

45=-5t^2+80t+1

We move all terms to the left:

45-(-5t^2+80t+1)=0

We get rid of parentheses

5t^2-80t-1+45=0

We add all the numbers together, and all the variables

5t^2-80t+44=0

a = 5; b = -80; c = +44;
Δ = b2-4ac
Δ = -802-4·5·44
Δ = 5520
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:

$\sqrt{\Delta}=\sqrt{5520}=\sqrt{16*345}=\sqrt{16}*\sqrt{345}=4\sqrt{345}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{345}}{2*5}=\frac{80-4\sqrt{345}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{345}}{2*5}=\frac{80+4\sqrt{345}}{10}
$