solution

a = 4.91
b = 9.7
h = 5
Solve[(.5*a + .5*(a^2/b))*j^2 - (a^2/b)*Sqrt[2*9.8*h]*j + .5(a^2/b)*2*9.8*5 -
a*9.8*5 == 0, j]


{{j -> -3.24562}, {j -> 9.89949}}


j^2/(2*9.8)

0.537451