Question

How do i solve this using the quadratic formula? (45 points)

Answer 1

`x=(1)/(3)\pm(2√(3))/(3)`

Explanation:

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