What two number add to 15 but multiply to 50

Assume two numbers, x and y

x + y = 15

xy = 50

y = 15 - x

x(15-x) = 50

15x- x^2 = 50

x^2 - 15x +  50 = 0 

(x-5)(x-10) = 0

either 
x = 5   -> y = 10

or 
x = 10 -> y = 5

The two numbers are 10, 5 

Let, the numbers = a, b

Then, a + b = 15
a * b = 50

Substitute the value of a from equation (1), 
(15-b) * b= 50
15b - b² = 50
b²-15b+50 = 0
b²-5b-10b+50 = 0
b(b-5) -10(b-5) = 0
(b-5)(b-10) = 0

b = 5 OR 10

In short, Your Numbers would be: 5 & 10

Hope this helps!

3batches is the answer