Solve 1/4(x^2)=1/6(3x-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 - \frac{3}{3} i, x_{2} = 1 + \frac{3}{3} i

Alternative Form

x_{1} \approx 1 - 0.57735 i, x_{2} \approx 1 + 0.57735 i

Evaluate

\frac{1}{4} x^{2} = \frac{1}{6} (3 x - 2)

Multiply the terms

More Steps

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

Move the expression to the left side

\frac{1}{4} x^{2} - \frac{1}{2} x + \frac{1}{3} = 0

Multiply both sides

12 (\frac{1}{4} x^{2} - \frac{1}{2} x + \frac{1}{3}) = 12 \times 0

Calculate

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

Substitute a= 3,b= - 6 and c= 4 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 4}{2 \times 3}

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{6 \pm - 12}{6}

Simplify the radical expression

More Steps

x = \frac{6 \pm 2 3 \times i}{6}

Separate the equation into 2 possible cases

x = \frac{6 + 2 3 \times i}{6} x = \frac{6 - 2 3 \times i}{6}

Simplify the expression

More Steps

x = 1 + \frac{3}{3} i x = \frac{6 - 2 3 \times i}{6}

Simplify the expression

More Steps

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

Solution

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

Alternative Form

x_{1} \approx 1 - 0.57735 i, x_{2} \approx 1 + 0.57735 i

Show Solution