Solve 17q-6q q-9q=15

Question

Solve the equation(The real numbers system)

q \in / R

Alternative Form

No real solution

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Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

q_{1} = \frac{2}{3} - \frac{74}{6} i, q_{2} = \frac{2}{3} + \frac{74}{6} i

Alternative Form

q_{1} \approx 0. \dot{6} - 1.433721 i, q_{2} \approx 0. \dot{6} + 1.433721 i

Evaluate

17 q - 6 q \times q - 9 q = 15

Simplify

More Steps

8 q - 6 q^{2} = 15

Move the expression to the left side

8 q - 6 q^{2} - 15 = 0

Rewrite in standard form

- 6 q^{2} + 8 q - 15 = 0

Multiply both sides

6 q^{2} - 8 q + 15 = 0

Substitute a= 6,b= - 8 and c= 15 into the quadratic formula q = \frac{- b \pm b ^{2} - 4 a c}{2 a}

q = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 6 \times 15}{2 \times 6}

Simplify the expression

q = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 6 \times 15}{12}

Simplify the expression

More Steps

q = \frac{8 \pm - 296}{12}

Simplify the radical expression

More Steps

q = \frac{8 \pm 2 74 \times i}{12}

Separate the equation into 2 possible cases

q = \frac{8 + 2 74 \times i}{12} q = \frac{8 - 2 74 \times i}{12}

Simplify the expression

More Steps

q = \frac{2}{3} + \frac{74}{6} i q = \frac{8 - 2 74 \times i}{12}

Simplify the expression

More Steps

q = \frac{2}{3} + \frac{74}{6} i q = \frac{2}{3} - \frac{74}{6} i

Solution

q_{1} = \frac{2}{3} - \frac{74}{6} i, q_{2} = \frac{2}{3} + \frac{74}{6} i

Alternative Form

q_{1} \approx 0. \dot{6} - 1.433721 i, q_{2} \approx 0. \dot{6} + 1.433721 i

Show Solution