Solve 9x^2-12x+4>0

$$9 x ^ { 2 } - 12 x + 4 > 0$$

Solve for x

$$x\neq \frac{2}{3}$$

Steps Using the Quadratic Formula

To solve the inequality, factor the left hand side. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$9x^{2}-12x+4=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 9 for a, -12 for b, and 4 for c in the quadratic formula.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 9\times 4}}{2\times 9}$$

Do the calculations.

$$x=\frac{12±0}{18}$$

Solutions are the same.

$$x=\frac{2}{3}$$

Rewrite the inequality by using the obtained solutions.

$$9\left(x-\frac{2}{3}\right)^{2}>0$$

Inequality holds for x\neq \frac{2}{3}.

$$x\neq \frac{2}{3}$$