4.9t^2=34.3t+3.5

Solution for 4.9t^2=34.3t+3.5 equation:

4.9t^2=34.3t+3.5

We move all terms to the left:

4.9t^2-(34.3t+3.5)=0

We get rid of parentheses

4.9t^2-34.3t-3.5=0

a = 4.9; b = -34.3; c = -3.5;
Δ = b2-4ac
Δ = -34.32-4·4.9·(-3.5)
Δ = 1245.09
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{-(-34.3)-\sqrt{1245.09}}{2*4.9}=\frac{34.3-\sqrt{1245.09}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34.3)+\sqrt{1245.09}}{2*4.9}=\frac{34.3+\sqrt{1245.09}}{9.8}
$