(t)=-4.9t^2+34.3t+4

Solution for (t)=-4.9t^2+34.3t+4 equation:

(t)=-4.9t^2+34.3t+4

We move all terms to the left:

(t)-(-4.9t^2+34.3t+4)=0

We get rid of parentheses

4.9t^2-34.3t+t-4=0

We add all the numbers together, and all the variables

4.9t^2-33.3t-4=0

a = 4.9; b = -33.3; c = -4;
Δ = b2-4ac
Δ = -33.32-4·4.9·(-4)
Δ = 1187.29
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{-(-33.3)-\sqrt{1187.29}}{2*4.9}=\frac{33.3-\sqrt{1187.29}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33.3)+\sqrt{1187.29}}{2*4.9}=\frac{33.3+\sqrt{1187.29}}{9.8}
$