Solve 3sqrt{2}x^2+sqrt{3}=0

$$3 \sqrt { 2 } x ^ { 2 } + \sqrt { 3 } = 0$$

Solve for x (complex solution)

$$x=-\frac{6^{\frac{3}{4}}i}{6}\approx -0-0.638943104i$$

$$x=\frac{6^{\frac{3}{4}}i}{6}\approx 0.638943104i$$

Steps by Finding Square Root

Subtract \sqrt{3} from both sides. Anything subtracted from zero gives its negation.

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

Dividing by 3\sqrt{2} undoes the multiplication by 3\sqrt{2}.

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

Divide -\sqrt{3} by 3\sqrt{2}.

$$x^{2}=-\frac{\sqrt{6}}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{6^{\frac{3}{4}}i}{6} x=-\frac{6^{\frac{3}{4}}i}{6}$$

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.

$$3\sqrt{2}x^{2}+\sqrt{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3\sqrt{2} for a, 0 for b, and \sqrt{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\sqrt{2}\sqrt{3}}}{2\times 3\sqrt{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\sqrt{2}\sqrt{3}}}{2\times 3\sqrt{2}}$$

Multiply -4 times 3\sqrt{2}.

$$x=\frac{0±\sqrt{\left(-12\sqrt{2}\right)\sqrt{3}}}{2\times 3\sqrt{2}}$$

Multiply -12\sqrt{2} times \sqrt{3}.

$$x=\frac{0±\sqrt{-12\sqrt{6}}}{2\times 3\sqrt{2}}$$

Take the square root of -12\sqrt{6}.

$$x=\frac{0±\sqrt[4]{54}\times \left(2i\right)}{2\times 3\sqrt{2}}$$

Multiply 2 times 3\sqrt{2}.

$$x=\frac{0±\sqrt[4]{54}\times \left(2i\right)}{6\sqrt{2}}$$

Now solve the equation x=\frac{0±\sqrt[4]{54}\times \left(2i\right)}{6\sqrt{2}} when ± is plus.

$$x=\frac{6^{\frac{3}{4}}i}{6}$$

Now solve the equation x=\frac{0±\sqrt[4]{54}\times \left(2i\right)}{6\sqrt{2}} when ± is minus.

$$x=-\frac{6^{\frac{3}{4}}i}{6}$$

The equation is now solved.

$$x=\frac{6^{\frac{3}{4}}i}{6} x=-\frac{6^{\frac{3}{4}}i}{6}$$