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9x^{2}-12x+4=0
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.
x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 9\times 4}}{2\times 9}
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{12±0}{18}
Do the calculations.
x=\frac{2}{3}
Solutions are the same.
9\left(x-\frac{2}{3}\right)^{2}\leq 0
Rewrite the inequality by using the obtained solutions.
x=\frac{2}{3}
Inequality holds for x=\frac{2}{3}.