Solve (2x 1)/3=(x^2)/4 (x - 4)/2

Question

Solve the equation

x_{1} = \frac{6 - 2 21}{3}, x_{2} = 0, x_{3} = \frac{6 + 2 21}{3}

Alternative Form

x_{1} \approx - 1.05505, x_{2} = 0, x_{3} \approx 5.05505

Evaluate

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

Multiply the terms

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

Multiply the terms

More Steps

\frac{2 x}{3} = \frac{x ^{2} ( x - 4 )}{8}

Cross multiply

2 x \times 8 = 3 x^{2} (x - 4)

Simplify the equation

16 x = 3 x^{2} (x - 4)

Expand the expression

More Steps

16 x = 3 x^{3} - 12 x^{2}

Move the expression to the left side

16 x - (3 x^{3} - 12 x^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

16 x - 3 x^{3} + 12 x^{2} = 0

Factor the expression

x (16 - 3 x^{2} + 12 x) = 0

Separate the equation into 2 possible cases

x = 0 16 - 3 x^{2} + 12 x = 0

Solve the equation

More Steps

x = 0 x = \frac{6 + 2 21}{3} x = \frac{6 - 2 21}{3}

Solution

x_{1} = \frac{6 - 2 21}{3}, x_{2} = 0, x_{3} = \frac{6 + 2 21}{3}

Alternative Form

x_{1} \approx - 1.05505, x_{2} = 0, x_{3} \approx 5.05505

Show Solution

Solve the equation

Graph