Solve y^2-3y^2=4

$$y ^ { 2 } - 3 y ^ { 2 } = 4$$

Solve for y

$$y=-\sqrt{2}i\approx -0-1.414213562i$$

$$y=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Combine y^{2} and -3y^{2} to get -2y^{2}.

$$-2y^{2}=4$$

Divide both sides by -2.

$$y^{2}=\frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$y^{2}=-2$$

The equation is now solved.

$$y=\sqrt{2}i y=-\sqrt{2}i$$

Steps Using the Quadratic Formula

Combine y^{2} and -3y^{2} to get -2y^{2}.

$$-2y^{2}=4$$

Subtract 4 from both sides.

$$-2y^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times -2.

$$y=\frac{0±\sqrt{8\left(-4\right)}}{2\left(-2\right)}$$

Multiply 8 times -4.

$$y=\frac{0±\sqrt{-32}}{2\left(-2\right)}$$

Take the square root of -32.

$$y=\frac{0±4\sqrt{2}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$y=\frac{0±4\sqrt{2}i}{-4}$$

Now solve the equation y=\frac{0±4\sqrt{2}i}{-4} when ± is plus.

$$y=-\sqrt{2}i$$

Now solve the equation y=\frac{0±4\sqrt{2}i}{-4} when ± is minus.

$$y=\sqrt{2}i$$

The equation is now solved.

$$y=-\sqrt{2}i y=\sqrt{2}i$$