8.3(t)=-4.9t^2+30.5t+8.3

Solution for 8.3(t)=-4.9t^2+30.5t+8.3 equation:

8.3(t)=-4.9t^2+30.5t+8.3

We move all terms to the left:

8.3(t)-(-4.9t^2+30.5t+8.3)=0

We get rid of parentheses

4.9t^2-30.5t+8.3t-8.3=0

We add all the numbers together, and all the variables

4.9t^2-22.2t-8.3=0

a = 4.9; b = -22.2; c = -8.3;
Δ = b2-4ac
Δ = -22.22-4·4.9·(-8.3)
Δ = 655.52
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{-(-22.2)-\sqrt{655.52}}{2*4.9}=\frac{22.2-\sqrt{655.52}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.2)+\sqrt{655.52}}{2*4.9}=\frac{22.2+\sqrt{655.52}}{9.8}
$