Solve 2x^2/9=7

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

Solve for x

$$x = \frac{3 \sqrt{14}}{2} \approx 5.61248608$$

$$x = -\frac{3 \sqrt{14}}{2} \approx -5.61248608$$

Steps by Finding Square Root

Multiply both sides by 9.

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

Multiply 7 and 9 to get 63.

$$2x^{2}=63$$

Divide both sides by 2.

$$x^{2}=\frac{63}{2}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides by 9.

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

Multiply 7 and 9 to get 63.

$$2x^{2}=63$$

Subtract 63 from both sides.

$$2x^{2}-63=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-63\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-63\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-63\right)}}{2\times 2}$$

Multiply -8 times -63.

$$x=\frac{0±\sqrt{504}}{2\times 2}$$

Take the square root of 504.

$$x=\frac{0±6\sqrt{14}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±6\sqrt{14}}{4}$$

Now solve the equation x=\frac{0±6\sqrt{14}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{14}}{4} when ± is minus.

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

The equation is now solved.

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