Solve frac{2sqrt{435}}{4-x}=y-3/2^3

$$\frac { 2 \sqrt { 435 } } { 4 - x } = \frac { y - 3 } { 2 ^ { 3 } }$$

Solve for x

$$x=-\frac{4\left(-y+4\sqrt{435}+3\right)}{y-3}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by -x+4.

$$2\sqrt{435}=\left(-\frac{1}{8}x+\frac{1}{2}\right)\left(y-3\right)$$

Use the distributive property to multiply -\frac{1}{8}x+\frac{1}{2} by y-3.

$$2\sqrt{435}=-\frac{1}{8}xy+\frac{3}{8}x+\frac{1}{2}y-\frac{3}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{8}xy+\frac{3}{8}x+\frac{1}{2}y-\frac{3}{2}=2\sqrt{435}$$

Subtract \frac{1}{2}y from both sides.

$$-\frac{1}{8}xy+\frac{3}{8}x-\frac{3}{2}=2\sqrt{435}-\frac{1}{2}y$$

Add \frac{3}{2} to both sides.

$$-\frac{1}{8}xy+\frac{3}{8}x=2\sqrt{435}-\frac{1}{2}y+\frac{3}{2}$$

Combine all terms containing x.

$$\left(-\frac{1}{8}y+\frac{3}{8}\right)x=2\sqrt{435}-\frac{1}{2}y+\frac{3}{2}$$

The equation is in standard form.

$$\frac{3-y}{8}x=-\frac{y}{2}+2\sqrt{435}+\frac{3}{2}$$

Divide both sides by -\frac{1}{8}y+\frac{3}{8}.

$$\frac{8\times \frac{3-y}{8}x}{3-y}=\frac{8\left(-\frac{y}{2}+2\sqrt{435}+\frac{3}{2}\right)}{3-y}$$

Dividing by -\frac{1}{8}y+\frac{3}{8} undoes the multiplication by -\frac{1}{8}y+\frac{3}{8}.

$$x=\frac{8\left(-\frac{y}{2}+2\sqrt{435}+\frac{3}{2}\right)}{3-y}$$

Divide 2\sqrt{435}-\frac{y}{2}+\frac{3}{2} by -\frac{1}{8}y+\frac{3}{8}.

$$x=4+\frac{16\sqrt{435}}{3-y}$$

Variable x cannot be equal to 4.

$$x=4+\frac{16\sqrt{435}}{3-y}\text{, }x\neq 4$$

Solve for y

$$y=-\frac{-3x+16\sqrt{435}+12}{x-4}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -x+4.

$$2\sqrt{435}=\left(-\frac{1}{8}x+\frac{1}{2}\right)\left(y-3\right)$$

Use the distributive property to multiply -\frac{1}{8}x+\frac{1}{2} by y-3.

$$2\sqrt{435}=-\frac{1}{8}xy+\frac{3}{8}x+\frac{1}{2}y-\frac{3}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{8}xy+\frac{3}{8}x+\frac{1}{2}y-\frac{3}{2}=2\sqrt{435}$$

Subtract \frac{3}{8}x from both sides.

$$-\frac{1}{8}xy+\frac{1}{2}y-\frac{3}{2}=2\sqrt{435}-\frac{3}{8}x$$

Add \frac{3}{2} to both sides.

$$-\frac{1}{8}xy+\frac{1}{2}y=2\sqrt{435}-\frac{3}{8}x+\frac{3}{2}$$

Combine all terms containing y.

$$\left(-\frac{1}{8}x+\frac{1}{2}\right)y=2\sqrt{435}-\frac{3}{8}x+\frac{3}{2}$$

The equation is in standard form.

$$\left(-\frac{x}{8}+\frac{1}{2}\right)y=-\frac{3x}{8}+2\sqrt{435}+\frac{3}{2}$$

Divide both sides by -\frac{1}{8}x+\frac{1}{2}.

$$\frac{\left(-\frac{x}{8}+\frac{1}{2}\right)y}{-\frac{x}{8}+\frac{1}{2}}=\frac{-\frac{3x}{8}+2\sqrt{435}+\frac{3}{2}}{-\frac{x}{8}+\frac{1}{2}}$$

Dividing by -\frac{1}{8}x+\frac{1}{2} undoes the multiplication by -\frac{1}{8}x+\frac{1}{2}.

$$y=\frac{-\frac{3x}{8}+2\sqrt{435}+\frac{3}{2}}{-\frac{x}{8}+\frac{1}{2}}$$

Divide 2\sqrt{435}-\frac{3x}{8}+\frac{3}{2} by -\frac{1}{8}x+\frac{1}{2}.

$$y=\frac{-3x+16\sqrt{435}+12}{4-x}$$