-4.9t2+39.2t+15=50

Solution for -4.9t2+39.2t+15=50 equation:

-4.9t^2+39.2t+15=50

We move all terms to the left:

-4.9t^2+39.2t+15-(50)=0

We add all the numbers together, and all the variables

-4.9t^2+39.2t-35=0

a = -4.9; b = 39.2; c = -35;
Δ = b2-4ac
Δ = 39.22-4·(-4.9)·(-35)
Δ = 850.64
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{-(39.2)-\sqrt{850.64}}{2*-4.9}=\frac{-39.2-\sqrt{850.64}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39.2)+\sqrt{850.64}}{2*-4.9}=\frac{-39.2+\sqrt{850.64}}{-9.8}
$