$\"\"$

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The equation is $\"\"$ .

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Subtract 11 from each side.

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$\"\"$

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$\"\"$

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Compare the equation with $\"\"$ .

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a = 4, b = 7 and c = $\"\"$ . $\"\"$

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a) Now we can find discriminant value

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$\"\"$ (Substitute a = 4, b = 7 and c = $\"\"$ )

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$\"\"$

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Product of two same sings is positive.

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$\"\"$

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$\"\"$

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$\"\"$

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b) The discriminant is positive, so the equation have two rational roots.

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c) Apply quadratic formula: $\"\"$

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$\"\"$ (Replace $\"\"$ , a with 4, and b with 7)

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The solutions are $\"\"$ . $\"\"$

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The discriminant value is 225 and the equation have two complex roots.

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The solutions are $\"\"$ .