9x²–7x–2=0

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

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

Here, \(a = 9\), \(b = -7\), and \(c = -2\).

1. Calculate \(b^2 - 4ac\):

\[ b^2 - 4ac = (-7)^2 - 4(9)(-2) = 49 + 72 = 121 \]

2. Since \(121\) is a perfect square, we take the square root:

\[ \sqrt{121} = 11 \]

3. Now substitute back into the quadratic formula:

\[ x = \frac{-(-7) \pm 11}{2(9)} = \frac{7 \pm 11}{18} \]

4. Calculate the two possible values for \(x\):

• For \(x_1\):

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