Solve 3(3k-10) 1=8(3/2k^2)

Question

Solve the equation(The real numbers system)

k \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

k_{1} = \frac{3}{8} - \frac{151}{8} i, k_{2} = \frac{3}{8} + \frac{151}{8} i

Alternative Form

k_{1} \approx 0.375 - 1.536026 i, k_{2} \approx 0.375 + 1.536026 i

Evaluate

3 (3 k - 10) \times 1 = 8 \times \frac{3}{2} k^{2}

Multiply the terms

3 (3 k - 10) = 8 \times \frac{3}{2} k^{2}

Multiply the numbers

More Steps

3 (3 k - 10) = 12 k^{2}

Swap the sides

12 k^{2} = 3 (3 k - 10)

Expand the expression

More Steps

12 k^{2} = 9 k - 30

Move the expression to the left side

12 k^{2} - 9 k + 30 = 0

Substitute a= 12,b= - 9 and c= 30 into the quadratic formula k = \frac{- b \pm b ^{2} - 4 a c}{2 a}

k = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 12 \times 30}{2 \times 12}

Simplify the expression

k = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 12 \times 30}{24}

Simplify the expression

More Steps

k = \frac{9 \pm - 1359}{24}

Simplify the radical expression

More Steps

k = \frac{9 \pm 3 151 \times i}{24}

Separate the equation into 2 possible cases

k = \frac{9 + 3 151 \times i}{24} k = \frac{9 - 3 151 \times i}{24}

Simplify the expression

More Steps

k = \frac{3}{8} + \frac{151}{8} i k = \frac{9 - 3 151 \times i}{24}

Simplify the expression

More Steps

k = \frac{3}{8} + \frac{151}{8} i k = \frac{3}{8} - \frac{151}{8} i

Solution

k_{1} = \frac{3}{8} - \frac{151}{8} i, k_{2} = \frac{3}{8} + \frac{151}{8} i

Alternative Form

k_{1} \approx 0.375 - 1.536026 i, k_{2} \approx 0.375 + 1.536026 i

Show Solution