(t)=-4.9t^2+16t+9

Solution for (t)=-4.9t^2+16t+9 equation:

(t)=-4.9t^2+16t+9

We move all terms to the left:

(t)-(-4.9t^2+16t+9)=0

We get rid of parentheses

4.9t^2-16t+t-9=0

We add all the numbers together, and all the variables

4.9t^2-15t-9=0

a = 4.9; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·4.9·(-9)
Δ = 401.4
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{-(-15)-\sqrt{401.4}}{2*4.9}=\frac{15-\sqrt{401.4}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{401.4}}{2*4.9}=\frac{15+\sqrt{401.4}}{9.8}
$