4.9t^2+9.8t=34.3

Solution for 4.9t^2+9.8t=34.3 equation:

4.9t^2+9.8t=34.3

We move all terms to the left:

4.9t^2+9.8t-(34.3)=0

We add all the numbers together, and all the variables

4.9t^2+9.8t-34.3=0

a = 4.9; b = 9.8; c = -34.3;
Δ = b2-4ac
Δ = 9.82-4·4.9·(-34.3)
Δ = 768.32
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{-(9.8)-\sqrt{768.32}}{2*4.9}=\frac{-9.8-\sqrt{768.32}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.8)+\sqrt{768.32}}{2*4.9}=\frac{-9.8+\sqrt{768.32}}{9.8}
$