Y=4.9t^2+14t+2.5

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

=4.9Y^2+14Y+2.5

We move all terms to the left:

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

We get rid of parentheses

-4.9Y^2-14Y-2.5=0

a = -4.9; b = -14; c = -2.5;
Δ = b2-4ac
Δ = -142-4·(-4.9)·(-2.5)
Δ = 147
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{147}=\sqrt{49*3}=\sqrt{49}*\sqrt{3}=7\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-7\sqrt{3}}{2*-4.9}=\frac{14-7\sqrt{3}}{-9.8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+7\sqrt{3}}{2*-4.9}=\frac{14+7\sqrt{3}}{-9.8}
$