Write as a Function of x x^2-4x=5x-6y

$x^{2} - 4 x = 5 x - 6 y$

Step 1

Rewrite the equation as $5 x - 6 y = x^{2} - 4 x$ .

$5 x - 6 y = x^{2} - 4 x$

Step 2

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

Subtract $5 x$ from both sides of the equation.

$- 6 y = x^{2} - 4 x - 5 x$

Subtract $5 x$ from $- 4 x$ .

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $- 9$ and $- 6$ .

Factor $- 3$ out of $- 9 x$ .

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

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

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

Write as a Function of x x^2-4x=5x-6y

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