Solve 12x-7-6x=5x^2

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

Show Solution

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}{5} - \frac{26}{5} i, x_{2} = \frac{3}{5} + \frac{26}{5} i

Alternative Form

x_{1} \approx 0.6 - 1.019804 i, x_{2} \approx 0.6 + 1.019804 i

Evaluate

12 x - 7 - 6 x = 5 x^{2}

Subtract the terms

More Steps

6 x - 7 = 5 x^{2}

Swap the sides

5 x^{2} = 6 x - 7

Move the expression to the left side

5 x^{2} - 6 x + 7 = 0

Substitute a= 5,b= - 6 and c= 7 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 5 \times 7}{2 \times 5}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 5 \times 7}{10}

Simplify the expression

More Steps

x = \frac{6 \pm - 104}{10}

Simplify the radical expression

More Steps

x = \frac{6 \pm 2 26 \times i}{10}

Separate the equation into 2 possible cases

x = \frac{6 + 2 26 \times i}{10} x = \frac{6 - 2 26 \times i}{10}

Simplify the expression

More Steps

x = \frac{3}{5} + \frac{26}{5} i x = \frac{6 - 2 26 \times i}{10}

Simplify the expression

More Steps

x = \frac{3}{5} + \frac{26}{5} i x = \frac{3}{5} - \frac{26}{5} i

Solution

x_{1} = \frac{3}{5} - \frac{26}{5} i, x_{2} = \frac{3}{5} + \frac{26}{5} i

Alternative Form

x_{1} \approx 0.6 - 1.019804 i, x_{2} \approx 0.6 + 1.019804 i

Show Solution