Solve 4(x^2)/2 =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 using the PQ formula in the complex numbers system

x_{1} = \frac{1}{3} - \frac{11}{3} i, x_{2} = \frac{1}{3} + \frac{11}{3} i

Alternative Form

x_{1} \approx 0. \dot{3} - 1.105542 i, x_{2} \approx 0. \dot{3} + 1.105542 i

Evaluate

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

Cancel out the common factor 2

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

Multiply the terms

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

Rewrite the expression

2 x^{2} = \frac{4}{3} x - \frac{8}{3}

Move the expression to the left side

2 x^{2} - \frac{4}{3} x + \frac{8}{3} = 0

Multiply both sides

3 (2 x^{2} - \frac{4}{3} x + \frac{8}{3}) = 3 \times 0

Calculate

6 x^{2} - 4 x + 8 = 0

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

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

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{4 \pm - 176}{12}

Simplify the radical expression

More Steps

x = \frac{4 \pm 4 11 \times i}{12}

Separate the equation into 2 possible cases

x = \frac{4 + 4 11 \times i}{12} x = \frac{4 - 4 11 \times i}{12}

Simplify the expression

More Steps

x = \frac{1}{3} + \frac{11}{3} i x = \frac{4 - 4 11 \times i}{12}

Simplify the expression

More Steps

x = \frac{1}{3} + \frac{11}{3} i x = \frac{1}{3} - \frac{11}{3} i

Solution

x_{1} = \frac{1}{3} - \frac{11}{3} i, x_{2} = \frac{1}{3} + \frac{11}{3} i

Alternative Form

x_{1} \approx 0. \dot{3} - 1.105542 i, x_{2} \approx 0. \dot{3} + 1.105542 i

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