Answer:
[tex]x=\frac{2}{3}[/tex]
x = 0
Step-by-step explanation:
Method 1: Quadratic Formula
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
3x² - 2x = 0
a = 3
b = - 2
c = 0
[tex]x=\frac{-(-2)±\sqrt{(-2)^{2}-4((3)(0)) } }{2(3)}[/tex]
[tex]x=\frac{-(-2)±\sqrt{4-4((3)(0)) } }{2(3)}[/tex]
[tex]x=\frac{-(-2)±\sqrt{4+0 } }{2(3)}[/tex]
[tex]x=\frac{2±\sqrt{4 } }{2(3)}[/tex]
[tex]x=\frac{2±2 }{2(3)}[/tex]
[tex]x=\frac{2±2 }{6}[/tex]
Two separate equations
[tex]x=\frac{2+2 }{6}[/tex]
[tex]x=\frac{2-2 }{6}[/tex]
[tex]x=\frac{4 }{6}[/tex]
[tex]x=\frac{2}{3}[/tex]
[tex]x=\frac{0 }{6}[/tex]
x = 0
Method 2: Factoring
3x² - 2x = 0
(3x - 2) · x = 0
Two separate equations
3x - 2 = 0
3x - 2 + 2 = 0 + 2
3x = 2
3x ÷ 3 = 2 ÷ 3
[tex]x=\frac{2}{3}[/tex]
x = 0
