0=-4.9t^2+12t+30

Solution for 0=-4.9t^2+12t+30 equation:

0=-4.9t^2+12t+30

We move all terms to the left:

0-(-4.9t^2+12t+30)=0

We add all the numbers together, and all the variables

-(-4.9t^2+12t+30)=0

We get rid of parentheses

4.9t^2-12t-30=0

a = 4.9; b = -12; c = -30;
Δ = b2-4ac
Δ = -122-4·4.9·(-30)
Δ = 732
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{183}}{2*4.9}=\frac{12-2\sqrt{183}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{183}}{2*4.9}=\frac{12+2\sqrt{183}}{9.8}
$