Solve 8xt^2=4/3(x+1)

$$8 x t ^ { 2 } = \frac { 4 } { 3 } ( x + 1 )$$

Solve for x (complex solution)

$$x=\frac{1}{6t^{2}-1}$$

$$t\neq -\frac{\sqrt{6}}{6}\text{ and }t\neq \frac{\sqrt{6}}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{3} by x+1.

$$8xt^{2}=\frac{4}{3}x+\frac{4}{3}$$

Subtract \frac{4}{3}x from both sides.

$$8xt^{2}-\frac{4}{3}x=\frac{4}{3}$$

Combine all terms containing x.

$$\left(8t^{2}-\frac{4}{3}\right)x=\frac{4}{3}$$

Divide both sides by 8t^{2}-\frac{4}{3}.

$$\frac{\left(8t^{2}-\frac{4}{3}\right)x}{8t^{2}-\frac{4}{3}}=\frac{\frac{4}{3}}{8t^{2}-\frac{4}{3}}$$

Dividing by 8t^{2}-\frac{4}{3} undoes the multiplication by 8t^{2}-\frac{4}{3}.

$$x=\frac{\frac{4}{3}}{8t^{2}-\frac{4}{3}}$$

Divide \frac{4}{3} by 8t^{2}-\frac{4}{3}.

$$x=\frac{1}{6t^{2}-1}$$

Solve for x

$$x=\frac{1}{6t^{2}-1}$$

$$|t|\neq \frac{\sqrt{6}}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{3} by x+1.

$$8xt^{2}=\frac{4}{3}x+\frac{4}{3}$$

Subtract \frac{4}{3}x from both sides.

$$8xt^{2}-\frac{4}{3}x=\frac{4}{3}$$

Combine all terms containing x.

$$\left(8t^{2}-\frac{4}{3}\right)x=\frac{4}{3}$$

Divide both sides by 8t^{2}-\frac{4}{3}.

$$\frac{\left(8t^{2}-\frac{4}{3}\right)x}{8t^{2}-\frac{4}{3}}=\frac{\frac{4}{3}}{8t^{2}-\frac{4}{3}}$$

Dividing by 8t^{2}-\frac{4}{3} undoes the multiplication by 8t^{2}-\frac{4}{3}.

$$x=\frac{\frac{4}{3}}{8t^{2}-\frac{4}{3}}$$

Divide \frac{4}{3} by 8t^{2}-\frac{4}{3}.

$$x=\frac{1}{6t^{2}-1}$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{6+\frac{6}{x}}}{6}$$

$$t=\frac{\sqrt{6+\frac{6}{x}}}{6}\text{, }x\neq 0$$

Solve for t

$$t=\frac{\sqrt{6+\frac{6}{x}}}{6}$$

$$t=-\frac{\sqrt{6+\frac{6}{x}}}{6}\text{, }x\leq -1\text{ or }x>0$$