Solve 4/3x=2.5x/7.5

$$\frac { 4 } { 3 x } = \frac { 2.5 x } { 7.5 }$$

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x.

$$4=3x\times \frac{2.5x}{7.5}$$

Divide 2.5x by 7.5 to get \frac{1}{3}x.

$$4=3x\times \frac{1}{3}x$$

Multiply 3 and \frac{1}{3} to get 1.

$$4=xx$$

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

$$4=x^{2}$$

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

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x.

$$4=3x\times \frac{2.5x}{7.5}$$

Divide 2.5x by 7.5 to get \frac{1}{3}x.

$$4=3x\times \frac{1}{3}x$$

Multiply 3 and \frac{1}{3} to get 1.

$$4=xx$$

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

$$4=x^{2}$$

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

$$x^{2}=4$$

Subtract 4 from both sides.

$$x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)}}{2}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16}}{2}$$

Take the square root of 16.

$$x=\frac{0±4}{2}$$

Now solve the equation x=\frac{0±4}{2} when ± is plus. Divide 4 by 2.

$$x=2$$

Now solve the equation x=\frac{0±4}{2} when ± is minus. Divide -4 by 2.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$