0=12.6+7t-4.90t^2

Solution for 0=12.6+7t-4.90t^2 equation:

0=12.6+7t-4.90t^2

We move all terms to the left:

0-(12.6+7t-4.90t^2)=0

We add all the numbers together, and all the variables

-(12.6+7t-4.90t^2)=0

We get rid of parentheses

4.90t^2-7t-12.6=0

a = 4.90; b = -7; c = -12.6;
Δ = b2-4ac
Δ = -72-4·4.90·(-12.6)
Δ = 295.96
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{-(-7)-\sqrt{295.96}}{2*4.90}=\frac{7-\sqrt{295.96}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{295.96}}{2*4.90}=\frac{7+\sqrt{295.96}}{9.8}
$