3=1+9t-5t^2

Solution for 3=1+9t-5t^2 equation:

3=1+9t-5t^2

We move all terms to the left:

3-(1+9t-5t^2)=0

We get rid of parentheses

5t^2-9t-1+3=0

We add all the numbers together, and all the variables

5t^2-9t+2=0

a = 5; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·5·2
Δ = 41
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{-(-9)-\sqrt{41}}{2*5}=\frac{9-\sqrt{41}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*5}=\frac{9+\sqrt{41}}{10}
$