63.4=9.8t^2+45t+1

Solution for 63.4=9.8t^2+45t+1 equation:

63.4=9.8t^2+45t+1

We move all terms to the left:

63.4-(9.8t^2+45t+1)=0

We get rid of parentheses

-9.8t^2-45t-1+63.4=0

We add all the numbers together, and all the variables

-9.8t^2-45t+62.4=0

a = -9.8; b = -45; c = +62.4;
Δ = b2-4ac
Δ = -452-4·(-9.8)·62.4
Δ = 4471.08
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{4471.08}}{2*-9.8}=\frac{45-\sqrt{4471.08}}{-19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{4471.08}}{2*-9.8}=\frac{45+\sqrt{4471.08}}{-19.6}
$