0=2.5+14t-4.9t^2

Solution for 0=2.5+14t-4.9t^2 equation:

0=2.5+14t-4.9t^2

We move all terms to the left:

0-(2.5+14t-4.9t^2)=0

We add all the numbers together, and all the variables

-(2.5+14t-4.9t^2)=0

We get rid of parentheses

4.9t^2-14t-2.5=0

a = 4.9; b = -14; c = -2.5;
Δ = b2-4ac
Δ = -142-4·4.9·(-2.5)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-7\sqrt{5}}{2*4.9}=\frac{14-7\sqrt{5}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+7\sqrt{5}}{2*4.9}=\frac{14+7\sqrt{5}}{9.8}
$