Solve 81x/7x/2=6

$$\frac{ 81x }{ 7 } \frac{ x }{ 2 } =6$$

Solve for x

$$x = \frac{2 \sqrt{21}}{9} \approx 1.018350154$$

$$x = -\frac{2 \sqrt{21}}{9} \approx -1.018350154$$

Steps by Finding Square Root

Multiply both sides of the equation by 14, the least common multiple of 7,2.

$$81xx=84$$

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

$$81x^{2}=84$$

Divide both sides by 81.

$$x^{2}=\frac{84}{81}$$

Reduce the fraction \frac{84}{81} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{28}{27}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{21}}{9} x=-\frac{2\sqrt{21}}{9}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 14, the least common multiple of 7,2.

$$81xx=84$$

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

$$81x^{2}=84$$

Subtract 84 from both sides.

$$81x^{2}-84=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 81 for a, 0 for b, and -84 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 81\left(-84\right)}}{2\times 81}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 81\left(-84\right)}}{2\times 81}$$

Multiply -4 times 81.

$$x=\frac{0±\sqrt{-324\left(-84\right)}}{2\times 81}$$

Multiply -324 times -84.

$$x=\frac{0±\sqrt{27216}}{2\times 81}$$

Take the square root of 27216.

$$x=\frac{0±36\sqrt{21}}{2\times 81}$$

Multiply 2 times 81.

$$x=\frac{0±36\sqrt{21}}{162}$$

Now solve the equation x=\frac{0±36\sqrt{21}}{162} when ± is plus.

$$x=\frac{2\sqrt{21}}{9}$$

Now solve the equation x=\frac{0±36\sqrt{21}}{162} when ± is minus.

$$x=-\frac{2\sqrt{21}}{9}$$

The equation is now solved.

$$x=\frac{2\sqrt{21}}{9} x=-\frac{2\sqrt{21}}{9}$$