Solve 4x/3=5/5x

$$\frac { 4 x } { 3 } = \frac { 5 } { 5 x }$$

Solve for x

$$x=\frac{\sqrt{3}}{2}\approx 0.866025404$$

$$x=-\frac{\sqrt{3}}{2}\approx -0.866025404$$

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 15x, the least common multiple of 3,5x.

$$5x\times 4x=3\times 5$$

Multiply 5 and 4 to get 20.

$$20xx=3\times 5$$

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

$$20x^{2}=3\times 5$$

Multiply 3 and 5 to get 15.

$$20x^{2}=15$$

Divide both sides by 20.

$$x^{2}=\frac{15}{20}$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{3}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{2} x=-\frac{\sqrt{3}}{2}$$

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 15x, the least common multiple of 3,5x.

$$5x\times 4x=3\times 5$$

Multiply 5 and 4 to get 20.

$$20xx=3\times 5$$

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

$$20x^{2}=3\times 5$$

Multiply 3 and 5 to get 15.

$$20x^{2}=15$$

Subtract 15 from both sides.

$$20x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-15\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-15\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-15\right)}}{2\times 20}$$

Multiply -80 times -15.

$$x=\frac{0±\sqrt{1200}}{2\times 20}$$

Take the square root of 1200.

$$x=\frac{0±20\sqrt{3}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±20\sqrt{3}}{40}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{40} when ± is plus.

$$x=\frac{\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{40} when ± is minus.

$$x=-\frac{\sqrt{3}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{2} x=-\frac{\sqrt{3}}{2}$$