Use the discriminant to determine the number and type of solutions of the following quadratic equation.
\[
-7 x^{2}-5 x+5=0
\]
Select the correct answer below:
There are two distinct rational solutions.
There are two distinct irrational solutions.
There are two complex solutions.
There is a single rational solution.

Step 1 ：Given the quadratic equation \(-7x^{2}-5x+5=0\), we can identify the coefficients as \(a = -7\), \(b = -5\), and \(c = 5\).

Step 2 ：We can calculate the discriminant using the formula \(b^{2} - 4ac\). Substituting the values of \(a\), \(b\), and \(c\) into the formula, we get a discriminant of 165.

Step 3 ：Since the discriminant is positive, the quadratic equation has two distinct real solutions. However, we need to check if these solutions are rational or irrational.

Step 4 ：A solution is rational if the square root of the discriminant is a perfect square, and irrational otherwise. Checking if 165 is a perfect square, we find that it is not.

Step 5 ：Since the square root of the discriminant is not a perfect square, the solutions of the quadratic equation are irrational. Therefore, the quadratic equation has two distinct irrational solutions.

Step 6 ：\(\boxed{\text{Final Answer: There are two distinct irrational solutions.}}\)