t=-4.9t^2+30.5t+9.4

Solution for t=-4.9t^2+30.5t+9.4 equation:

t=-4.9t^2+30.5t+9.4

We move all terms to the left:

t-(-4.9t^2+30.5t+9.4)=0

We get rid of parentheses

4.9t^2-30.5t+t-9.4=0

We add all the numbers together, and all the variables

4.9t^2-29.5t-9.4=0

a = 4.9; b = -29.5; c = -9.4;
Δ = b2-4ac
Δ = -29.52-4·4.9·(-9.4)
Δ = 1054.49
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{-(-29.5)-\sqrt{1054.49}}{2*4.9}=\frac{29.5-\sqrt{1054.49}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29.5)+\sqrt{1054.49}}{2*4.9}=\frac{29.5+\sqrt{1054.49}}{9.8}
$