3=2+9t-5t^2

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

3=2+9t-5t^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5t^2-9t+1=0

a = 5; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·5·1
Δ = 61
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{61}}{2*5}=\frac{9-\sqrt{61}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{61}}{2*5}=\frac{9+\sqrt{61}}{10}
$