Solve for y
y=\frac{x\left(x+4\right)}{6}
Solve for x (complex solution)
x=-\sqrt{6y+4}-2
x=\sqrt{6y+4}-2
Solve for x
x=-\sqrt{6y+4}-2
x=\sqrt{6y+4}-2\text{, }y\geq -\frac{2}{3}
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-x^{2}-4x+5y+y=0
Add y to both sides.
-x^{2}-4x+6y=0
Combine 5y and y to get 6y.
-4x+6y=x^{2}
Add x^{2} to both sides. Anything plus zero gives itself.
6y=x^{2}+4x
Add 4x to both sides.
\frac{6y}{6}=\frac{x\left(x+4\right)}{6}
Divide both sides by 6.
y=\frac{x\left(x+4\right)}{6}
Dividing by 6 undoes the multiplication by 6.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}