Solve x^2-6/x=x+3/2

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

Solve for x

$$x=-4$$

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, the least common multiple of x,2.

$$2\left(x^{2}-6\right)=2xx+2x\times \frac{3}{2}$$

Use the distributive property to multiply 2 by x^{2}-6.

$$2x^{2}-12=2xx+2x\times \frac{3}{2}$$

Multiply x and x to get x^{2}.

$$2x^{2}-12=2x^{2}+2x\times \frac{3}{2}$$

Multiply 2 and \frac{3}{2} to get 3.

$$2x^{2}-12=2x^{2}+3x$$

Subtract 2x^{2} from both sides.

$$2x^{2}-12-2x^{2}=3x$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-12=3x$$

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

$$3x=-12$$

Divide both sides by 3.

$$x=\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$x=-4$$