Solve 9/7x^2-8=0

$$\frac { 9 } { 7 } x ^ { 2 } - 8 = 0$$

Solve for x

$$x = \frac{2 \sqrt{14}}{3} \approx 2.494438258$$

$$x = -\frac{2 \sqrt{14}}{3} \approx -2.494438258$$

Steps by Finding Square Root

Add 8 to both sides. Anything plus zero gives itself.

$$\frac{9}{7}x^{2}=8$$

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

$$x^{2}=8\times \frac{7}{9}$$

Multiply 8 and \frac{7}{9} to get \frac{56}{9}.

$$x^{2}=\frac{56}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{14}}{3} x=-\frac{2\sqrt{14}}{3}$$

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.

$$\frac{9}{7}x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{9}{7} for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{9}{7}\left(-8\right)}}{2\times \frac{9}{7}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{9}{7}\left(-8\right)}}{2\times \frac{9}{7}}$$

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

$$x=\frac{0±\sqrt{-\frac{36}{7}\left(-8\right)}}{2\times \frac{9}{7}}$$

Multiply -\frac{36}{7} times -8.

$$x=\frac{0±\sqrt{\frac{288}{7}}}{2\times \frac{9}{7}}$$

Take the square root of \frac{288}{7}.

$$x=\frac{0±\frac{12\sqrt{14}}{7}}{2\times \frac{9}{7}}$$

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

$$x=\frac{0±\frac{12\sqrt{14}}{7}}{\frac{18}{7}}$$

Now solve the equation x=\frac{0±\frac{12\sqrt{14}}{7}}{\frac{18}{7}} when ± is plus.

$$x=\frac{2\sqrt{14}}{3}$$

Now solve the equation x=\frac{0±\frac{12\sqrt{14}}{7}}{\frac{18}{7}} when ± is minus.

$$x=-\frac{2\sqrt{14}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{14}}{3} x=-\frac{2\sqrt{14}}{3}$$