Solve (2x-3):3=(x^2):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 using the PQ formula in the complex numbers system

x_{1} = \frac{2}{3} - \frac{14}{3} i, x_{2} = \frac{2}{3} + \frac{14}{3} i

Alternative Form

x_{1} \approx 0. \dot{6} - 1.247219 i, x_{2} \approx 0. \dot{6} + 1.247219 i

Evaluate

(2 x - 3) \div 3 = x^{2} \div 2

Rewrite the expression

\frac{2 x - 3}{3} = x^{2} \div 2

Rewrite the expression

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

Swap the sides

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

Rewrite the expression

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

Rewrite the expression

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

Move the expression to the left side

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

Multiply both sides

6 (\frac{1}{2} x^{2} - \frac{2}{3} x + 1) = 6 \times 0

Calculate

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

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

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

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{4 \pm - 56}{6}

Simplify the radical expression

More Steps

x = \frac{4 \pm 2 14 \times i}{6}

Separate the equation into 2 possible cases

x = \frac{4 + 2 14 \times i}{6} x = \frac{4 - 2 14 \times i}{6}

Simplify the expression

More Steps

x = \frac{2}{3} + \frac{14}{3} i x = \frac{4 - 2 14 \times i}{6}

Simplify the expression

More Steps

x = \frac{2}{3} + \frac{14}{3} i x = \frac{2}{3} - \frac{14}{3} i

Solution

x_{1} = \frac{2}{3} - \frac{14}{3} i, x_{2} = \frac{2}{3} + \frac{14}{3} i

Alternative Form

x_{1} \approx 0. \dot{6} - 1.247219 i, x_{2} \approx 0. \dot{6} + 1.247219 i

Show Solution