$\"\"$

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The solutions of a quadratic equation $\"\"$ can be classified as follows.

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If the discriminant $\"\"$ is

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1. positive, then the quadratic equation has two distinct real solutions and and its graph has two x - intercepts.

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2. zero, then the quadratic equation has one repeated real solution and its graph has one x - intercept.

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3. negative, then the quadratic equation has no real solutions and its graph has no x - intercepts.

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$\"\"$

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The quadratic equation is $\"\"$ .

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$\"\"$

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Add $\"\"$ to each side.

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$\"\"$

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$\"\"$

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Subtract $\"\"$ from each side.

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$\"\"$

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$\"\"$

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Subtract 9 from each side.

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$\"\"$

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$\"\"$ .

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The general form of quadratic equation is $\"\"$ .

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The discriminant formula is $\"\"$ .

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Consider $\"\"$ .

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Compare it with general form.

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$\"\"$

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Substitute the values of $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Since the discriminant is positive, the quadratic equation has two distinct real solutions and its graph has two x - intercepts.

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$\"\"$

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The quadratic equation has two distinct real solutions.