Solve 3=(9+y^2/2)

$$3 = ( \frac { 9 + y ^ { 2 } } { 2 } )$$

Solve for y

$$y=-\sqrt{3}i\approx -0-1.732050808i$$

$$y=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Multiply both sides by 2.

$$3\times 2=9+y^{2}$$

Multiply 3 and 2 to get 6.

$$6=9+y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$9+y^{2}=6$$

Subtract 9 from both sides.

$$y^{2}=6-9$$

Subtract 9 from 6 to get -3.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$3\times 2=9+y^{2}$$

Multiply 3 and 2 to get 6.

$$6=9+y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$9+y^{2}=6$$

Subtract 6 from both sides.

$$9+y^{2}-6=0$$

Subtract 6 from 9 to get 3.

$$3+y^{2}=0$$

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.

$$y^{2}+3=0$$

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

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

Square 0.

$$y=\frac{0±\sqrt{-4\times 3}}{2}$$

Multiply -4 times 3.

$$y=\frac{0±\sqrt{-12}}{2}$$

Take the square root of -12.

$$y=\frac{0±2\sqrt{3}i}{2}$$

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

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

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

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

The equation is now solved.

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