Solve x^2-2/5=3/6

$$\frac { x ^ { 2 } - 2 } { 5 } = \frac { 3 } { 6 }$$

Solve for x

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

Steps by Finding Square Root

Multiply both sides of the equation by 30, the least common multiple of 5,6.

$$6\left(x^{2}-2\right)=5\times 3$$

Use the distributive property to multiply 6 by x^{2}-2.

$$6x^{2}-12=5\times 3$$

Multiply 5 and 3 to get 15.

$$6x^{2}-12=15$$

Add 12 to both sides.

$$6x^{2}=15+12$$

Add 15 and 12 to get 27.

$$6x^{2}=27$$

Divide both sides by 6.

$$x^{2}=\frac{27}{6}$$

Reduce the fraction \frac{27}{6} to lowest terms by extracting and canceling out 3.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by 30, the least common multiple of 5,6.

$$6\left(x^{2}-2\right)=5\times 3$$

Use the distributive property to multiply 6 by x^{2}-2.

$$6x^{2}-12=5\times 3$$

Multiply 5 and 3 to get 15.

$$6x^{2}-12=15$$

Subtract 15 from both sides.

$$6x^{2}-12-15=0$$

Subtract 15 from -12 to get -27.

$$6x^{2}-27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-27\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-27\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-27\right)}}{2\times 6}$$

Multiply -24 times -27.

$$x=\frac{0±\sqrt{648}}{2\times 6}$$

Take the square root of 648.

$$x=\frac{0±18\sqrt{2}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±18\sqrt{2}}{12}$$

Now solve the equation x=\frac{0±18\sqrt{2}}{12} when ± is plus.

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

Now solve the equation x=\frac{0±18\sqrt{2}}{12} when ± is minus.

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

The equation is now solved.

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