Solve 2/2x(7n-3)^2=4

$$\frac { 2 } { 2 x } ( 7 n - 3 ) ^ { 2 } = 4$$

Solve for x

$$x=\frac{\left(7n-3\right)^{2}}{4}$$

$$n\neq \frac{3}{7}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x.

$$2\left(7n-3\right)^{2}=8x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7n-3\right)^{2}.

$$2\left(49n^{2}-42n+9\right)=8x$$

Use the distributive property to multiply 2 by 49n^{2}-42n+9.

$$98n^{2}-84n+18=8x$$

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

$$8x=98n^{2}-84n+18$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{2\left(7n-3\right)^{2}}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{2\left(7n-3\right)^{2}}{8}$$

Divide 2\left(-3+7n\right)^{2} by 8.

$$x=\frac{\left(7n-3\right)^{2}}{4}$$

Variable x cannot be equal to 0.

$$x=\frac{\left(7n-3\right)^{2}}{4}\text{, }x\neq 0$$

Solve for n (complex solution)

$$n=\frac{2\sqrt{x}+3}{7}$$

$$n=\frac{-2\sqrt{x}+3}{7}\text{, }x\neq 0$$

Solve for n

$$n=\frac{-2\sqrt{x}+3}{7}$$

$$n=\frac{2\sqrt{x}+3}{7}\text{, }x>0$$