Finite Math Examples

$3 x^{2} - 9 y + 6 = 0$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Add $9 y$ to both sides of the equation.

$3 x^{2} + 6 = 9 y$

Step 1.2

Subtract $6$ from both sides of the equation.

$3 x^{2} = 9 y - 6$

Step 2

Divide each term in $3 x^{2} = 9 y - 6$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x^{2} = 9 y - 6$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{9 y}{3} + \frac{- 6}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{9 y}{3} + \frac{- 6}{3}$

Step 2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{9 y}{3} + \frac{- 6}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $9$ and $3$ .

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Step 2.3.1.1.1

Factor $3$ out of $9 y$ .

$x^{2} = \frac{3 (3 y)}{3} + \frac{- 6}{3}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $3$ out of $3$ .

$x^{2} = \frac{3 (3 y)}{3 (1)} + \frac{- 6}{3}$

Step 2.3.1.1.2.2

Cancel the common factor.

$x^{2} = \frac{3 (3 y)}{3 \cdot 1} + \frac{- 6}{3}$

Step 2.3.1.1.2.3

Rewrite the expression.

$x^{2} = \frac{3 y}{1} + \frac{- 6}{3}$

Step 2.3.1.1.2.4

Divide $3 y$ by $1$ .

$x^{2} = 3 y + \frac{- 6}{3}$

Step 2.3.1.2

Divide $- 6$ by $3$ .

$x^{2} = 3 y - 2$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{3 y - 2}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{3 y - 2}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{3 y - 2}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{3 y - 2}$

$x = - \sqrt{3 y - 2}$

$x = \sqrt{3 y - 2}$

$x = - \sqrt{3 y - 2}$