Solve x^2+5/6xx-4/6=0

$$x ^ { 2 } + \frac { 5 } { 6 } x x - \frac { 4 } { 6 } = 0$$

Solve for x

$$x=\frac{2\sqrt{11}}{11}\approx 0.603022689$$

$$x=-\frac{2\sqrt{11}}{11}\approx -0.603022689$$

Steps by Finding Square Root

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

$$x^{2}+\frac{5}{6}x^{2}-\frac{4}{6}=0$$

Combine x^{2} and \frac{5}{6}x^{2} to get \frac{11}{6}x^{2}.

$$\frac{11}{6}x^{2}-\frac{4}{6}=0$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{11}{6}x^{2}-\frac{2}{3}=0$$

Add \frac{2}{3} to both sides. Anything plus zero gives itself.

$$\frac{11}{6}x^{2}=\frac{2}{3}$$

Multiply both sides by \frac{6}{11}, the reciprocal of \frac{11}{6}.

$$x^{2}=\frac{2}{3}\times \frac{6}{11}$$

Multiply \frac{2}{3} and \frac{6}{11} to get \frac{4}{11}.

$$x^{2}=\frac{4}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{11}}{11} x=-\frac{2\sqrt{11}}{11}$$

Steps Using the Quadratic Formula

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

$$x^{2}+\frac{5}{6}x^{2}-\frac{4}{6}=0$$

Combine x^{2} and \frac{5}{6}x^{2} to get \frac{11}{6}x^{2}.

$$\frac{11}{6}x^{2}-\frac{4}{6}=0$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{11}{6}x^{2}-\frac{2}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{11}{6} for a, 0 for b, and -\frac{2}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{11}{6}\left(-\frac{2}{3}\right)}}{2\times \frac{11}{6}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{11}{6}\left(-\frac{2}{3}\right)}}{2\times \frac{11}{6}}$$

Multiply -4 times \frac{11}{6}.

$$x=\frac{0±\sqrt{-\frac{22}{3}\left(-\frac{2}{3}\right)}}{2\times \frac{11}{6}}$$

Multiply -\frac{22}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{44}{9}}}{2\times \frac{11}{6}}$$

Take the square root of \frac{44}{9}.

$$x=\frac{0±\frac{2\sqrt{11}}{3}}{2\times \frac{11}{6}}$$

Multiply 2 times \frac{11}{6}.

$$x=\frac{0±\frac{2\sqrt{11}}{3}}{\frac{11}{3}}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{11}}{3}}{\frac{11}{3}} when ± is plus.

$$x=\frac{2\sqrt{11}}{11}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{11}}{3}}{\frac{11}{3}} when ± is minus.

$$x=-\frac{2\sqrt{11}}{11}$$

The equation is now solved.

$$x=\frac{2\sqrt{11}}{11} x=-\frac{2\sqrt{11}}{11}$$