Find the real solutions, if any, for the following equation. Use any method. \( 10 x^{2}+9 x-9=0 \) Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. The solution set is \{ \}. (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The solution is not a real number.

To solve the quadratic equation \( 10x^{2} + 9x - 9 = 0 \), we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 10 \), \( b = 9 \), and \( c = -9 \). First, we calculate the discriminant: \( b^2 - 4ac = 9^2 - 4(10)(-9) = 81 + 360 = 441 \). Since the discriminant is positive, we can find two real solutions. Now we calculate: \( x = \frac{-9 \pm \sqrt{441}}{2(10)} = \frac{-9 \pm 21}{20} \). Thus, the solutions are \( x = \frac{12}{20} = \frac{3}{5} \) and \( x = \frac{-30}{20} = -\frac{3}{2} \). So the solution set is \( \left\{ \frac{3}{5}, -\frac{3}{2} \right\} \). A. The solution set is \( \left\{ \frac{3}{5}, -\frac{3}{2} \right\} \).