Solve y=9x^4-bx^2

$$y = 9 x ^ { 4 } - b x ^ { 2 }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{9x^{4}-y}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$9x^{4}-bx^{2}=y$$

Subtract 9x^{4} from both sides.

$$-bx^{2}=y-9x^{4}$$

The equation is in standard form.

$$\left(-x^{2}\right)b=y-9x^{4}$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)b}{-x^{2}}=\frac{y-9x^{4}}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$b=\frac{y-9x^{4}}{-x^{2}}$$

Divide y-9x^{4} by -x^{2}.

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

Solve for b

$$\left\{\begin{matrix}b=\frac{9x^{4}-y}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$9x^{4}-bx^{2}=y$$

Subtract 9x^{4} from both sides.

$$-bx^{2}=y-9x^{4}$$

The equation is in standard form.

$$\left(-x^{2}\right)b=y-9x^{4}$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)b}{-x^{2}}=\frac{y-9x^{4}}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$b=\frac{y-9x^{4}}{-x^{2}}$$

Divide y-9x^{4} by -x^{2}.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{2\left(\sqrt{36y+b^{2}}+b\right)}}{6}$$

$$x=-\frac{\sqrt{2\left(\sqrt{36y+b^{2}}+b\right)}}{6}$$

$$x=-\frac{\sqrt{2\left(-\sqrt{36y+b^{2}}+b\right)}}{6}$$

$$x=\frac{\sqrt{2\left(-\sqrt{36y+b^{2}}+b\right)}}{6}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{2\left(-\sqrt{36y+b^{2}}+b\right)}}{6}\text{; }x=\frac{\sqrt{2\left(-\sqrt{36y+b^{2}}+b\right)}}{6}\text{, }&\left(b>0\text{ and }y\leq 0\text{ and }y\geq -\frac{b^{2}}{36}\right)\text{ or }\left(y=0\text{ and }b\geq 0\right)\\x=-\frac{\sqrt{2\left(\sqrt{36y+b^{2}}+b\right)}}{6}\text{; }x=\frac{\sqrt{2\left(\sqrt{36y+b^{2}}+b\right)}}{6}\text{, }&\left(y>-\frac{b^{2}}{36}\text{ and }y\geq 0\right)\text{ or }\left(y=0\text{ and }b\geq 0\right)\text{ or }\left(b>0\text{ and }y\geq -\frac{b^{2}}{36}\right)\end{matrix}\right.$$