Solve 5/6x^2-10/9=0

$$\frac { 5 } { 6 } x ^ { 2 } - \frac { 10 } { 9 } = 0$$

Solve for x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

Add \frac{10}{9} to both sides. Anything plus zero gives itself.

$$\frac{5}{6}x^{2}=\frac{10}{9}$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$x^{2}=\frac{10}{9}\times \frac{6}{5}$$

Multiply \frac{10}{9} and \frac{6}{5} to get \frac{4}{3}.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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.

$$\frac{5}{6}x^{2}-\frac{10}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{5}{6} for a, 0 for b, and -\frac{10}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{5}{6}\left(-\frac{10}{9}\right)}}{2\times \frac{5}{6}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{5}{6}\left(-\frac{10}{9}\right)}}{2\times \frac{5}{6}}$$

Multiply -4 times \frac{5}{6}.

$$x=\frac{0±\sqrt{-\frac{10}{3}\left(-\frac{10}{9}\right)}}{2\times \frac{5}{6}}$$

Multiply -\frac{10}{3} times -\frac{10}{9} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{100}{27}}}{2\times \frac{5}{6}}$$

Take the square root of \frac{100}{27}.

$$x=\frac{0±\frac{10\sqrt{3}}{9}}{2\times \frac{5}{6}}$$

Multiply 2 times \frac{5}{6}.

$$x=\frac{0±\frac{10\sqrt{3}}{9}}{\frac{5}{3}}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{3}}{9}}{\frac{5}{3}} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{10\sqrt{3}}{9}}{\frac{5}{3}} when ± is minus.

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

The equation is now solved.

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