What times what equals 30 but add to get 40?

Lets call those two unknown numbers a, b and write the info in the problem as equations:

a*b = 30

a + b = 40

lets solve for a in the second equation and substitute in the first:

a + b = 40

a = 40 - b

therefore:

a*b = 30

(40 - b) b = 30

40b - b^2 = 30

b^2 - 40b + 30 = 0

if we apply the general quadratic equation to solve we have:

b = (40 + - √ (1600 - 120)) / 2

b = (40 + - √ (1480)) / 2

b = (40 + - 38.47) / 2

There are two solutions:

b1 = (40 + 38.47) / 2

b1 = 39.24

b2 = (40 - 38.47) / 2

b2 = 0.765

lets use the second solution b2 = 0.765, and substitute in the first equation to find a:

a*b = 30

a*0.765 = 30

a = 30/0.765

a = 39.216

so the numbers are 39.216 and 0.765

(15x2) = 30, (30 + 10) = 40 ... (P. E. M. D. A. S)