45.9=30t-4.9t^2

Solution for 45.9=30t-4.9t^2 equation:

45.9=30t-4.9t^2

We move all terms to the left:

45.9-(30t-4.9t^2)=0

We get rid of parentheses

4.9t^2-30t+45.9=0

a = 4.9; b = -30; c = +45.9;
Δ = b2-4ac
Δ = -302-4·4.9·45.9
Δ = 0.36000000000001
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{-(-30)-\sqrt{0.36000000000001}}{2*4.9}=\frac{30-\sqrt{0.36000000000001}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{0.36000000000001}}{2*4.9}=\frac{30+\sqrt{0.36000000000001}}{9.8}
$