Solve 3/4 1/2 (x- 4/3 )= 3/5 x 5/4 (x 2/3 )

Question

Solve the equation(The real numbers system)

x \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

x_{1} = \frac{3}{8} - \frac{55}{8} i, x_{2} = \frac{3}{8} + \frac{55}{8} i

Alternative Form

x_{1} \approx 0.375 - 0.927025 i, x_{2} \approx 0.375 + 0.927025 i

Evaluate

\frac{3}{4} \times \frac{1}{2} (x - \frac{4}{3}) = \frac{3}{5} x \times \frac{5}{4} (x \times \frac{2}{3})

Remove the parentheses

\frac{3}{4} \times \frac{1}{2} (x - \frac{4}{3}) = \frac{3}{5} x \times \frac{5}{4} x \times \frac{2}{3}

Multiply the terms

More Steps

\frac{3}{8} x - \frac{1}{2} = \frac{3}{5} x \times \frac{5}{4} x \times \frac{2}{3}

Multiply

More Steps

\frac{3}{8} x - \frac{1}{2} = \frac{1}{2} x^{2}

Swap the sides

\frac{1}{2} x^{2} = \frac{3}{8} x - \frac{1}{2}

Move the expression to the left side

\frac{1}{2} x^{2} - \frac{3}{8} x + \frac{1}{2} = 0

Multiply both sides

8 (\frac{1}{2} x^{2} - \frac{3}{8} x + \frac{1}{2}) = 8 \times 0

Calculate

4 x^{2} - 3 x + 4 = 0

Substitute a= 4,b= - 3 and c= 4 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 4 \times 4}{2 \times 4}

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 4 \times 4}{8}

Simplify the expression

More Steps

x = \frac{3 \pm - 55}{8}

Simplify the radical expression

More Steps

x = \frac{3 \pm 55 \times i}{8}

Separate the equation into 2 possible cases

x = \frac{3 + 55 \times i}{8} x = \frac{3 - 55 \times i}{8}

Simplify the expression

x = \frac{3}{8} + \frac{55}{8} i x = \frac{3 - 55 \times i}{8}

Simplify the expression

x = \frac{3}{8} + \frac{55}{8} i x = \frac{3}{8} - \frac{55}{8} i

Solution

x_{1} = \frac{3}{8} - \frac{55}{8} i, x_{2} = \frac{3}{8} + \frac{55}{8} i

Alternative Form

x_{1} \approx 0.375 - 0.927025 i, x_{2} \approx 0.375 + 0.927025 i

Show Solution