Solve 192/x=3x/4

$$\frac { 192 } { x } = \frac { 3 x } { 4 }$$

Solve for x

$$x=16$$

$$x=-16$$

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 4x, the least common multiple of x,4.

$$4\times 192=x\times 3x$$

Multiply 4 and 192 to get 768.

$$768=x\times 3x$$

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

$$768=x^{2}\times 3$$

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

$$x^{2}\times 3=768$$

Divide both sides by 3.

$$x^{2}=\frac{768}{3}$$

Divide 768 by 3 to get 256.

$$x^{2}=256$$

Take the square root of both sides of the equation.

$$x=16 x=-16$$

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 4x, the least common multiple of x,4.

$$4\times 192=x\times 3x$$

Multiply 4 and 192 to get 768.

$$768=x\times 3x$$

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

$$768=x^{2}\times 3$$

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

$$x^{2}\times 3=768$$

Subtract 768 from both sides.

$$x^{2}\times 3-768=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3x^{2}-768=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -768 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-768\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-768\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-768\right)}}{2\times 3}$$

Multiply -12 times -768.

$$x=\frac{0±\sqrt{9216}}{2\times 3}$$

Take the square root of 9216.

$$x=\frac{0±96}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±96}{6}$$

Now solve the equation x=\frac{0±96}{6} when ± is plus. Divide 96 by 6.

$$x=16$$

Now solve the equation x=\frac{0±96}{6} when ± is minus. Divide -96 by 6.

$$x=-16$$

The equation is now solved.

$$x=16 x=-16$$