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

Question

Solve the equation

x_{1} = - \frac{2}{3}, x_{2} = \frac{5}{4}

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 1.25

Evaluate

x^{2} - (7 \times \frac{x}{12}) = \frac{5}{6}

Multiply the terms

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

Multiply both sides of the equation by LCD

(x^{2} - \frac{7 x}{12}) \times 12 = \frac{5}{6} \times 12

Simplify the equation

More Steps

Evaluate

(x^{2} - \frac{7 x}{12}) \times 12

Apply the distributive property

x^{2} \times 12 - \frac{7 x}{12} \times 12

Simplify

x^{2} \times 12 - 7 x

Use the commutative property to reorder the terms

12 x^{2} - 7 x

12 x^{2} - 7 x = \frac{5}{6} \times 12

Simplify the equation

More Steps

Evaluate

\frac{5}{6} \times 12

Simplify

5 \times 2

Multiply the numbers

10

12 x^{2} - 7 x = 10

Move the expression to the left side

12 x^{2} - 7 x - 10 = 0

Factor the expression

More Steps

Evaluate

12 x^{2} - 7 x - 10

Rewrite the expression

12 x^{2} + (- 15 + 8) x - 10

Calculate

12 x^{2} - 15 x + 8 x - 10

Rewrite the expression

3 x \times 4 x - 3 x \times 5 + 2 \times 4 x - 2 \times 5

Factor out 3 x from the expression

3 x (4 x - 5) + 2 \times 4 x - 2 \times 5

Factor out 2 from the expression

3 x (4 x - 5) + 2 (4 x - 5)

Factor out 4 x - 5 from the expression

(3 x + 2) (4 x - 5)

(3 x + 2) (4 x - 5) = 0

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

3 x + 2 = 0 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

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

Divide the numbers

x = \frac{- 2}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{2}{3}

x = - \frac{2}{3} 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 5 = 0

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

4 x = 0 + 5

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

4 x = 5

Divide both sides

\frac{4 x}{4} = \frac{5}{4}

Divide the numbers

x = \frac{5}{4}

x = - \frac{2}{3} x = \frac{5}{4}

Solution

x_{1} = - \frac{2}{3}, x_{2} = \frac{5}{4}

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 1.25

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