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

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

Alternative Form

x_{1} \approx 1 - 1.732051 i, x_{2} \approx 1 + 1.732051 i

Evaluate

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

Multiply the terms

More Steps

\frac{x ( 3 x - 2 )}{8} = \frac{x - 3}{2}

Rewrite the expression

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

Rewrite the expression

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

Move the expression to the left side

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

Multiply both sides

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

Calculate

3 x^{2} - 6 x + 12 = 0

Substitute a= 3,b= - 6 and c= 12 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 3 \times 12}{2 \times 3}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 3 \times 12}{6}

Simplify the expression

More Steps

x = \frac{6 \pm - 108}{6}

Simplify the radical expression

More Steps

x = \frac{6 \pm 6 3 \times i}{6}

Separate the equation into 2 possible cases

x = \frac{6 + 6 3 \times i}{6} x = \frac{6 - 6 3 \times i}{6}

Simplify the expression

More Steps

x = 1 + 3 \times i x = \frac{6 - 6 3 \times i}{6}

Simplify the expression

More Steps

x = 1 + 3 \times i x = 1 - 3 \times i

Solution

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

Alternative Form

x_{1} \approx 1 - 1.732051 i, x_{2} \approx 1 + 1.732051 i

Show Solution