Solve 3(5x^2) = 2(3x - 6)

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{1}{5} - \frac{19}{5} i, x_{2} = \frac{1}{5} + \frac{19}{5} i

Alternative Form

x_{1} \approx 0.2 - 0.87178 i, x_{2} \approx 0.2 + 0.87178 i

Evaluate

3 \times 5 x^{2} = 2 (3 x - 6)

Multiply the numbers

15 x^{2} = 2 (3 x - 6)

Expand the expression

More Steps

15 x^{2} = 6 x - 12

Move the expression to the left side

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

Substitute a= 15,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 15 \times 12}{2 \times 15}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 15 \times 12}{30}

Simplify the expression

More Steps

x = \frac{6 \pm - 684}{30}

Simplify the radical expression

More Steps

x = \frac{6 \pm 6 19 \times i}{30}

Separate the equation into 2 possible cases

x = \frac{6 + 6 19 \times i}{30} x = \frac{6 - 6 19 \times i}{30}

Simplify the expression

More Steps

x = \frac{1}{5} + \frac{19}{5} i x = \frac{6 - 6 19 \times i}{30}

Simplify the expression

More Steps

x = \frac{1}{5} + \frac{19}{5} i x = \frac{1}{5} - \frac{19}{5} i

Solution

x_{1} = \frac{1}{5} - \frac{19}{5} i, x_{2} = \frac{1}{5} + \frac{19}{5} i

Alternative Form

x_{1} \approx 0.2 - 0.87178 i, x_{2} \approx 0.2 + 0.87178 i

Show Solution