Solve 2y(4y)=3-4

$$2 y ( 4 y ) = 3 - 4$$

Solve for y

$$y=-\frac{\sqrt{2}i}{4}\approx -0-0.353553391i$$

$$y=\frac{\sqrt{2}i}{4}\approx 0.353553391i$$

Steps by Finding Square Root

Multiply y and y to get y^{2}.

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

Multiply 2 and 4 to get 8.

$$8y^{2}=3-4$$

Subtract 4 from 3 to get -1.

$$8y^{2}=-1$$

Divide both sides by 8.

$$y^{2}=-\frac{1}{8}$$

The equation is now solved.

$$y=\frac{\sqrt{2}i}{4} y=-\frac{\sqrt{2}i}{4}$$

Steps Using the Quadratic Formula

Multiply y and y to get y^{2}.

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

Multiply 2 and 4 to get 8.

$$8y^{2}=3-4$$

Subtract 4 from 3 to get -1.

$$8y^{2}=-1$$

Add 1 to both sides.

$$8y^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 8}}{2\times 8}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 8}}{2\times 8}$$

Multiply -4 times 8.

$$y=\frac{0±\sqrt{-32}}{2\times 8}$$

Take the square root of -32.

$$y=\frac{0±4\sqrt{2}i}{2\times 8}$$

Multiply 2 times 8.

$$y=\frac{0±4\sqrt{2}i}{16}$$

Now solve the equation y=\frac{0±4\sqrt{2}i}{16} when ± is plus.

$$y=\frac{\sqrt{2}i}{4}$$

Now solve the equation y=\frac{0±4\sqrt{2}i}{16} when ± is minus.

$$y=-\frac{\sqrt{2}i}{4}$$

The equation is now solved.

$$y=\frac{\sqrt{2}i}{4} y=-\frac{\sqrt{2}i}{4}$$