Solve 3/3x^2=-3/4

$$\frac { 3 } { 3 } x ^ { 2 } = - \frac { 3 } { 4 }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}i}{2}\approx -0-0.866025404i$$

$$x=\frac{\sqrt{3}i}{2}\approx 0.866025404i$$

Steps by Finding Square Root

Divide 3 by 3 to get 1.

$$1x^{2}=-\frac{3}{4}$$

Divide both sides by 1.

$$x^{2}=\frac{-\frac{3}{4}}{1}$$

Express \frac{-\frac{3}{4}}{1} as a single fraction.

$$x^{2}=\frac{-3}{4\times 1}$$

Multiply 4 and 1 to get 4.

$$x^{2}=\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$x^{2}=-\frac{3}{4}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Divide 3 by 3 to get 1.

$$1x^{2}=-\frac{3}{4}$$

Add \frac{3}{4} to both sides.

$$1x^{2}+\frac{3}{4}=0$$

Reorder the terms.

$$x^{2}+\frac{3}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{3}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times \frac{3}{4}.

$$x=\frac{0±\sqrt{-3}}{2}$$

Take the square root of -3.

$$x=\frac{0±\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±\sqrt{3}i}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\sqrt{3}i}{2} when ± is minus.

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

The equation is now solved.

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