You probably want to rewrite the equation to give you the number of sides.

d = s(s-3)/2

2d = s(s-3)

s

s = (3 ±√(3

s = (3 +√(9+8d))/2 (probably only the positive root is useful)

For d = 119, this is

s = (3 +√(9+8*119))/2 = (3+√961)/2 = (3+31)/2 = 34/2 = 17

Your polygon has 17 sides.

Check

d = 17(17-3)/2 = 17*14/2 = 17*7 = 119

d = s(s-3)/2

2d = s(s-3)

s

^{2}-3s -2d = 0 (this is the standard form of a quadratic equation. You use the quadratic formula to solve it.)s = (3 ±√(3

^{2}- 4*(1)(-2d)))/(2*(1))s = (3 +√(9+8d))/2 (probably only the positive root is useful)

For d = 119, this is

s = (3 +√(9+8*119))/2 = (3+√961)/2 = (3+31)/2 = 34/2 = 17

Your polygon has 17 sides.

Check

d = 17(17-3)/2 = 17*14/2 = 17*7 = 119