Answer:
[tex]x=\frac{1}{3}\pm\frac{2\sqrt{3}}{3}[/tex]
Step-by-step explanation:
[tex]\newline{\text{The quadratic equation is as follows:}}\newline{\text{If you have } ax^2+bx+c=0, \text{ then } x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}\bigskip\newline{\text{Given } 9x^2-11=6x \text{, we need to make one side equal to 0}}\newline{\text{subtract 6x from both sides to get} 9x^2-6x-11=0}\newline{\text{Therefor } a=9 \text{, } b=-6 \text{, and} c=-11}\newline{\text{If we use the quadratic formula, we get}}\newline{x=\frac{-(-6)\pm\sqrt{(-6)^2-4(9)(11)}}{2(9)}}\newline{x=\frac{6\pm\sqrt{36+396}}{18}}\newline{x=\frac{6\pm\sqrt{432}}{18}}\newline{x=\frac{6\pm{}12\sqrt{3}}{18}}\newline{x=\frac{1\pm{}2\sqrt{3}}{3}}\newline{x=\frac{1}{3}\pm\frac{2\sqrt{3}}{3}}\newline{\text{So the answers are } x=\frac{1}{3}+\frac{2\sqrt{3}}{3} \text{ and } x=\frac{1}{3}-\frac{2\sqrt{3}}{3}[/tex]
