Solve x^2=-9/2y

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

Solve for y

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

Steps for Solving Linear Equation

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

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

Divide both sides of the equation by -\frac{9}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by -\frac{9}{2} undoes the multiplication by -\frac{9}{2}.

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

Divide x^{2} by -\frac{9}{2} by multiplying x^{2} by the reciprocal of -\frac{9}{2}.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\frac{3\sqrt{-2y}}{2}\text{, }y\leq 0$$