To find the value of the discriminant for the quadratic equation \(9h^2 - 6 = 7h\), we first need to rearrange it into the standard form of a quadratic equation, which is \(ax^2 + bx + c = 0\).
- Rearranging the given equation: \[ 9h^2 - 7h - 6 = 0 \]
Here, the coefficients are:
- \(a = 9\)
- \(b = -7\)
- \(c = -6\)
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The discriminant \(D\) of a quadratic equation is given by the formula: \[ D = b^2 - 4ac \]
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Substituting in our values: \[ D = (-7)^2 - 4(9)(-6) \] \[ D = 49 - 4(9)(-6) \] \[ D = 49 - 4 \cdot 9 \cdot -6 \] \[ D = 49 + 216 \] \[ D = 265 \]
Thus, the value of the discriminant is \(265\).