Simplify \(\frac{4}{3}x\) to \(\frac{4x}{3}\).
Factor with quadratic formula.
In general, given \(a{x}^{2}+bx+c\), the factored form is:
\[a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})\]
In this case, \(a=1\), \(b=-\frac{4}{3}\) and \(c=\frac{4}{9}\).
\[(x-\frac{\frac{4}{3}+\sqrt{{(-\frac{4}{3})}^{2}-4\times \frac{4}{9}}}{2})(x-\frac{\frac{4}{3}-\sqrt{{(-\frac{4}{3})}^{2}-4\times \frac{4}{9}}}{2})\]
Simplify.
\[(x-\frac{2}{3})(x-\frac{2}{3})\]
Solve for \(x\).
Ask: When will \((x-\frac{2}{3})(x-\frac{2}{3})\) equal zero?
When \(x-\frac{2}{3}=0\) or \(x-\frac{2}{3}=0\)
Solve each of the 2 equations above.
\[x=\frac{2}{3}\]
