Solve 12x-7=7x^2 - ScanMath

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{6}{7} - \frac{13}{7} i, x_{2} = \frac{6}{7} + \frac{13}{7} i

Alternative Form

x_{1} \approx 0. \dot{8} 5714 \dot{2} - 0.515079 i, x_{2} \approx 0. \dot{8} 5714 \dot{2} + 0.515079 i

Evaluate

12 x - 7 = 7 x^{2}

Swap the sides

7 x^{2} = 12 x - 7

Move the expression to the left side

7 x^{2} - 12 x + 7 = 0

Substitute a= 7,b= - 12 and c= 7 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 7 \times 7}{2 \times 7}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 7 \times 7}{14}

Simplify the expression

More Steps

x = \frac{12 \pm - 52}{14}

Simplify the radical expression

More Steps

x = \frac{12 \pm 2 13 \times i}{14}

Separate the equation into 2 possible cases

x = \frac{12 + 2 13 \times i}{14} x = \frac{12 - 2 13 \times i}{14}

Simplify the expression

More Steps

x = \frac{6}{7} + \frac{13}{7} i x = \frac{12 - 2 13 \times i}{14}

Simplify the expression

More Steps

x = \frac{6}{7} + \frac{13}{7} i x = \frac{6}{7} - \frac{13}{7} i

Solution

x_{1} = \frac{6}{7} - \frac{13}{7} i, x_{2} = \frac{6}{7} + \frac{13}{7} i

Alternative Form

x_{1} \approx 0. \dot{8} 5714 \dot{2} - 0.515079 i, x_{2} \approx 0. \dot{8} 5714 \dot{2} + 0.515079 i

Show Solution