Solve for x (complex solution)
x=\frac{3}{y^{2}+6y+10}
y\neq -3+i\text{ and }y\neq -3-i
Solve for x
x=\frac{3}{y^{2}+6y+10}
Solve for y (complex solution)
y=\frac{\sqrt{x\left(3-x\right)}-3x}{x}
y=-\frac{\sqrt{x\left(3-x\right)}+3x}{x}\text{, }x\neq 0
Solve for y
y=\sqrt{-1+\frac{3}{x}}-3
y=-\sqrt{-1+\frac{3}{x}}-3\text{, }x>0\text{ and }x\leq 3
Graph
Share
Copied to clipboard
xy^{2}+6xy+10x=3
Add 3 to both sides. Anything plus zero gives itself.
\left(y^{2}+6y+10\right)x=3
Combine all terms containing x.
\frac{\left(y^{2}+6y+10\right)x}{y^{2}+6y+10}=\frac{3}{y^{2}+6y+10}
Divide both sides by y^{2}+6y+10.
x=\frac{3}{y^{2}+6y+10}
Dividing by y^{2}+6y+10 undoes the multiplication by y^{2}+6y+10.
xy^{2}+6xy+10x=3
Add 3 to both sides. Anything plus zero gives itself.
\left(y^{2}+6y+10\right)x=3
Combine all terms containing x.
\frac{\left(y^{2}+6y+10\right)x}{y^{2}+6y+10}=\frac{3}{y^{2}+6y+10}
Divide both sides by y^{2}+6y+10.
x=\frac{3}{y^{2}+6y+10}
Dividing by y^{2}+6y+10 undoes the multiplication by y^{2}+6y+10.
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}