Question

3x . (x-2)=2.(x+3/2)

Answer 1

3x (x - 2) = 2 (x + 3/2)
3x² - 6x = 2x + 6/2
3x² - 6x - 2x - 6/2 = 0
3x² - 8x - 3 = 0
a = 3, b = -8, c = -3

Δ = b² - 4ac
Δ = (-8)² - 4 . 3 . (-3)
Δ = 64 + 36
Δ = 100

x = $\frac{-b \pm \sqrt{\Delta} }{2a}$
x = $\frac{-(-8) \pm \sqrt{100} }{2 . 3}$
x = $\frac{8 \pm 10}{6}$

x₁ = $\frac{8 + 10}{6} = \frac{18}{6}$ = 3
x₂ = $\frac{8 - 10}{6} = \frac{-2}{6} (: 2) = -1/3$

S = {3, $\frac{-1}{3}$}