Solve y^2=3/4(2)-6

$$y ^ { 2 } = \frac { 3 } { 4 } ( 2 ) - 6$$

Solve for y

$$y=-\frac{3\sqrt{2}i}{2}\approx -0-2.121320344i$$

$$y=\frac{3\sqrt{2}i}{2}\approx 2.121320344i$$

Steps by Finding Square Root

Multiply \frac{3}{4} and 2 to get \frac{3}{2}.

$$y^{2}=\frac{3}{2}-6$$

Subtract 6 from \frac{3}{2} to get -\frac{9}{2}.

$$y^{2}=-\frac{9}{2}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Multiply \frac{3}{4} and 2 to get \frac{3}{2}.

$$y^{2}=\frac{3}{2}-6$$

Subtract 6 from \frac{3}{2} to get -\frac{9}{2}.

$$y^{2}=-\frac{9}{2}$$

Add \frac{9}{2} to both sides.

$$y^{2}+\frac{9}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{9}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times \frac{9}{2}}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times \frac{9}{2}}}{2}$$

Multiply -4 times \frac{9}{2}.

$$y=\frac{0±\sqrt{-18}}{2}$$

Take the square root of -18.

$$y=\frac{0±3\sqrt{2}i}{2}$$

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

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

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

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

The equation is now solved.

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