Solve for y (complex solution)
\left\{\begin{matrix}y=-\frac{5x}{6}+\frac{z}{6x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=-\frac{5x}{6}+\frac{z}{6x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
x=\frac{-\sqrt{9y^{2}+5z}-3y}{5}
x=\frac{\sqrt{9y^{2}+5z}-3y}{5}
Solve for x
x=\frac{-\sqrt{9y^{2}+5z}-3y}{5}
x=\frac{\sqrt{9y^{2}+5z}-3y}{5}\text{, }z\geq -\frac{9y^{2}}{5}
Share
Copied to clipboard
5x^{2}+6xy=z
Swap sides so that all variable terms are on the left hand side.
6xy=z-5x^{2}
Subtract 5x^{2} from both sides.
\frac{6xy}{6x}=\frac{z-5x^{2}}{6x}
Divide both sides by 6x.
y=\frac{z-5x^{2}}{6x}
Dividing by 6x undoes the multiplication by 6x.
y=-\frac{5x}{6}+\frac{z}{6x}
Divide z-5x^{2} by 6x.
5x^{2}+6xy=z
Swap sides so that all variable terms are on the left hand side.
6xy=z-5x^{2}
Subtract 5x^{2} from both sides.
\frac{6xy}{6x}=\frac{z-5x^{2}}{6x}
Divide both sides by 6x.
y=\frac{z-5x^{2}}{6x}
Dividing by 6x undoes the multiplication by 6x.
y=-\frac{5x}{6}+\frac{z}{6x}
Divide z-5x^{2} by 6x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}