To determine how many real solutions the equation \( 9h^2 - 6 = 7h \) has, we can first rewrite it in standard form:
\[ 9h^2 - 7h - 6 = 0 \]
The discriminant \( D \) of a quadratic equation in the form \( ax^2 + bx + c = 0 \) is given by:
\[ D = b^2 - 4ac \]
For our equation \( 9h^2 - 7h - 6 = 0 \), the coefficients are:
- \( a = 9 \)
- \( b = -7 \)
- \( c = -6 \)
Now we can calculate the discriminant:
\[ D = (-7)^2 - 4 \cdot 9 \cdot (-6) \] \[ D = 49 - 4 \cdot 9 \cdot (-6) \] \[ D = 49 + 216 \] \[ D = 265 \]
Since the discriminant \( D \) is greater than zero (\( D > 0 \)), this means that the quadratic equation has two real solutions.
Therefore, the answer is:
Two real solutions.