Solve 7/9x^2-6=0

$$\frac { 7 } { 9 } x ^ { 2 } - 6 = 0$$

Solve for x

$$x = \frac{3 \sqrt{42}}{7} \approx 2.777460299$$

$$x = -\frac{3 \sqrt{42}}{7} \approx -2.777460299$$

Steps by Finding Square Root

Add 6 to both sides. Anything plus zero gives itself.

$$\frac{7}{9}x^{2}=6$$

Multiply both sides by \frac{9}{7}, the reciprocal of \frac{7}{9}.

$$x^{2}=6\times \frac{9}{7}$$

Multiply 6 and \frac{9}{7} to get \frac{54}{7}.

$$x^{2}=\frac{54}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{42}}{7} x=-\frac{3\sqrt{42}}{7}$$

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.

$$\frac{7}{9}x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{7}{9} for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{7}{9}\left(-6\right)}}{2\times \frac{7}{9}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{7}{9}\left(-6\right)}}{2\times \frac{7}{9}}$$

Multiply -4 times \frac{7}{9}.

$$x=\frac{0±\sqrt{-\frac{28}{9}\left(-6\right)}}{2\times \frac{7}{9}}$$

Multiply -\frac{28}{9} times -6.

$$x=\frac{0±\sqrt{\frac{56}{3}}}{2\times \frac{7}{9}}$$

Take the square root of \frac{56}{3}.

$$x=\frac{0±\frac{2\sqrt{42}}{3}}{2\times \frac{7}{9}}$$

Multiply 2 times \frac{7}{9}.

$$x=\frac{0±\frac{2\sqrt{42}}{3}}{\frac{14}{9}}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{42}}{3}}{\frac{14}{9}} when ± is plus.

$$x=\frac{3\sqrt{42}}{7}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{42}}{3}}{\frac{14}{9}} when ± is minus.

$$x=-\frac{3\sqrt{42}}{7}$$

The equation is now solved.

$$x=\frac{3\sqrt{42}}{7} x=-\frac{3\sqrt{42}}{7}$$