let the quadratic equation be

ax^2 + bx + c = 0, where a,b,c are constants

we know that for x=0 the value is -3 that is

a*0^2 + b*0 + c = -3

c = -3

Now we need to find a and b.

Since -3 and 1/5 are the roots if we replace for x = -3 or x = 1/5 the value must be 0 that is

for x = -3

a(-3)^2 - 3b - 3 = 0

9a - 3b - 3 = 0

for x = 1/5

a(1/5)^2 + b(1/5) - 3 = 0

a/25 + b/5 - 3 = 0

by solving the system of equations

9a - 3b - 3 = 0

a/25 + b/5 - 3 = 0

we find

a = 5

b = 14

therefore the quadratic equation is

5x^2 + 14x - 3 = 0