Solve 6x^2-18=0

$$6 { x }^{ 2 } -18=0$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Add 18 to both sides. Anything plus zero gives itself.

$$6x^{2}=18$$

Divide both sides by 6.

$$x^{2}=\frac{18}{6}$$

Divide 18 by 6 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

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

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.

$$6x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-18\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-18\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-18\right)}}{2\times 6}$$

Multiply -24 times -18.

$$x=\frac{0±\sqrt{432}}{2\times 6}$$

Take the square root of 432.

$$x=\frac{0±12\sqrt{3}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±12\sqrt{3}}{12}$$

Now solve the equation x=\frac{0±12\sqrt{3}}{12} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±12\sqrt{3}}{12} when ± is minus.

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

The equation is now solved.

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