# How do you solve the quadratic using the quadratic formula given 9x^2-11=6x?

Oct 27, 2016

We put our equation into standard form, then use the quadratic equation to find

$x = \frac{1 \pm 2 \sqrt{3}}{3} \cong 1.49 , - 0.821$

#### Explanation:

To use the quadratic formula, we must first put our equation into the standard form:

$a {x}^{2} + b x + c = 0$

We can do this by subtracting $6 x$ from both sides of our equation yielding:

$9 {x}^{2} - 6 x - 11 = 0$

This allows us to match up the values

$a = 9 , b = - 6 \text{ }$ and $\text{ } c = - 11$

Then we use the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} = \frac{6 \pm \sqrt{36 - 4 \cdot 9 \cdot \left(- 11\right)}}{18}$

$x = \frac{6 \pm \sqrt{432}}{18} = \frac{1 \pm 2 \sqrt{3}}{3}$

$x \cong 1.49 , - 0.821$