30=6.14t+4.9t^2

Solution for 30=6.14t+4.9t^2 equation:

30=6.14t+4.9t^2

We move all terms to the left:

30-(6.14t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-6.14t+30=0

a = -4.9; b = -6.14; c = +30;
Δ = b2-4ac
Δ = -6.142-4·(-4.9)·30
Δ = 625.6996
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{-(-6.14)-\sqrt{625.6996}}{2*-4.9}=\frac{6.14-\sqrt{625.6996}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.14)+\sqrt{625.6996}}{2*-4.9}=\frac{6.14+\sqrt{625.6996}}{-9.8}
$