9x^2-7x-2=0

To solve the quadratic equation \(9x^2 - 7x - 2 = 0\), we can use the quadratic formula:

For an equation of the form \(ax^2 + bx + c = 0\), the solutions are given by:

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

In this case, \(a = 9\), \(b = -7\), and \(c = -2\). Substituting these values into the formula, we get:

\[x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(9)(-2)}}{2(9)}\]

\[x = \frac{7 \pm \sqrt{49 + 72}}{18}\]

\[x = \frac{7 \pm \sqrt{121}}{18}\]

\[x = \frac{7 \pm 11}{18}\]

So the solutions are:

\[x_1 = \frac{7 + 11}{18} = \frac{18}{18} = 1\]

\[x_2 = \frac{7 - 11}{18} = \frac{-4}{18} = -\frac{2}{9}\]

Therefore, the solutions to the equation \(9x^2 - 7x - 2 = 0\) are \(x = 1\) and \(x = -\frac{2}{9}\).