Find the exact solutions for (x/2+1/3)(x/4+1/5)=1/6?

Answer 1

One can simplify and reduce the equation:

(x/2 + 1/3)(x/4 + 1/5) = 1/6.................(1)

into the simplest quadratic equation form:

15x² + 22x - 12 = 0..................(2)

[To get rid of fractions multiply both sides of (1) by 120:

[(6)(x/2 + 1/3)][(20)(x/4 + 1/5)] = (1/6)(120)

(3x + 2)(5x + 4) = 20 or 15x² + 22x + 8 - 20 = 0

15x² + 22x - 12 = 0].

Solving (2) as quadratic:

x = [- 11 ± √ (301)]/15 or x ≈ 0.42327 or x ≈ - 1.8899

Answer 2

(3x + 2)(x/4 + 1/5) = 1
(3x + 2) (5x + 4) = 20
15x² + 22x + 8 = 20
15x² + 22x - 12 = 0
x = [- 22 ± √(22² + 720) ] / 30
x = [- 22 ± √1204 ] / 30
x = [- 22 ± 34.7 ] / 30
x = 12.7 / 30 , x = - 56.7 / 30
x = 0.423 , x = - 1.89