Solve 3/2x=10x/6

$$\frac{ 3 }{ 2x } = \frac{ 10x }{ 6 }$$

Solve for x

$$x=\frac{3\sqrt{10}}{10}\approx 0.948683298$$

$$x=-\frac{3\sqrt{10}}{10}\approx -0.948683298$$

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 6x, the least common multiple of 2x,6.

$$3\times 3=x\times 10x$$

Multiply 3 and 3 to get 9.

$$9=x\times 10x$$

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

$$9=x^{2}\times 10$$

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

$$x^{2}\times 10=9$$

Divide both sides by 10.

$$x^{2}=\frac{9}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{10} x=-\frac{3\sqrt{10}}{10}$$

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 6x, the least common multiple of 2x,6.

$$3\times 3=x\times 10x$$

Multiply 3 and 3 to get 9.

$$9=x\times 10x$$

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

$$9=x^{2}\times 10$$

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

$$x^{2}\times 10=9$$

Subtract 9 from both sides.

$$x^{2}\times 10-9=0$$

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.

$$10x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-9\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-9\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-9\right)}}{2\times 10}$$

Multiply -40 times -9.

$$x=\frac{0±\sqrt{360}}{2\times 10}$$

Take the square root of 360.

$$x=\frac{0±6\sqrt{10}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±6\sqrt{10}}{20}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{20} when ± is plus.

$$x=\frac{3\sqrt{10}}{10}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{20} when ± is minus.

$$x=-\frac{3\sqrt{10}}{10}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{10} x=-\frac{3\sqrt{10}}{10}$$