50=15t+4.9t^2

Solution for 50=15t+4.9t^2 equation:

50=15t+4.9t^2

We move all terms to the left:

50-(15t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-15t+50=0

a = -4.9; b = -15; c = +50;
Δ = b2-4ac
Δ = -152-4·(-4.9)·50
Δ = 1205
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{-(-15)-\sqrt{1205}}{2*-4.9}=\frac{15-\sqrt{1205}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1205}}{2*-4.9}=\frac{15+\sqrt{1205}}{-9.8}
$