Solve 7/3x 1/3x=4 5/3x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 0, x_{2} = \frac{51}{7}

Alternative Form

x_{1} = 0, x_{2} = 7. \dot{2} 8571 \dot{4}

Evaluate

\frac{7}{3} x \times \frac{1}{3} x = 4 \frac{5}{3} \times x

Multiply

More Steps

Evaluate

\frac{7}{3} x \times \frac{1}{3} x

Multiply the terms

More Steps

Evaluate

\frac{7}{3} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7}{3 \times 3}

Multiply the numbers

\frac{7}{9}

\frac{7}{9} x \times x

Multiply the terms

\frac{7}{9} x^{2}

\frac{7}{9} x^{2} = 4 \frac{5}{3} \times x

Covert the mixed number to an improper fraction

More Steps

Evaluate

4 \frac{5}{3}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{4 \times 3 + 5}{3}

Multiply the terms

\frac{12 + 5}{3}

Add the terms

\frac{17}{3}

\frac{7}{9} x^{2} = \frac{17}{3} x

Move the expression to the left side

\frac{7}{9} x^{2} - \frac{17}{3} x = 0

Factor the expression

More Steps

Evaluate

\frac{7}{9} x^{2} - \frac{17}{3} x

Rewrite the expression

\frac{1}{9} x \times 7 x - \frac{1}{9} x \times 51

Factor out \frac{1}{9} x from the expression

\frac{1}{9} x (7 x - 51)

\frac{1}{9} x (7 x - 51) = 0

When the product of factors equals 0,at least one factor is 0

7 x - 51 = 0 \frac{1}{9} x = 0

Solve the equation for x

More Steps

Evaluate

7 x - 51 = 0

Move the constant to the right-hand side and change its sign

7 x = 0 + 51

Removing 0 doesn't change the value,so remove it from the expression

7 x = 51

Divide both sides

\frac{7 x}{7} = \frac{51}{7}

Divide the numbers

x = \frac{51}{7}

x = \frac{51}{7} \frac{1}{9} x = 0

Solve the equation for x

x = \frac{51}{7} x = 0

Solution

x_{1} = 0, x_{2} = \frac{51}{7}

Alternative Form

x_{1} = 0, x_{2} = 7. \dot{2} 8571 \dot{4}

Show Solution