Solve for p (complex solution)
\left\{\begin{matrix}p=\frac{x}{6}+\frac{y}{2x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for p
\left\{\begin{matrix}p=\frac{x}{6}+\frac{y}{2x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
x=\sqrt{9p^{2}-3y}+3p
x=-\sqrt{9p^{2}-3y}+3p
Solve for x
x=\sqrt{9p^{2}-3y}+3p
x=-\sqrt{9p^{2}-3y}+3p\text{, }y\leq 3p^{2}
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-6px+3y=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
-6px=-x^{2}-3y
Subtract 3y from both sides.
\left(-6x\right)p=-x^{2}-3y
The equation is in standard form.
\frac{\left(-6x\right)p}{-6x}=\frac{-x^{2}-3y}{-6x}
Divide both sides by -6x.
p=\frac{-x^{2}-3y}{-6x}
Dividing by -6x undoes the multiplication by -6x.
p=\frac{x}{6}+\frac{y}{2x}
Divide -x^{2}-3y by -6x.
-6px+3y=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
-6px=-x^{2}-3y
Subtract 3y from both sides.
\left(-6x\right)p=-x^{2}-3y
The equation is in standard form.
\frac{\left(-6x\right)p}{-6x}=\frac{-x^{2}-3y}{-6x}
Divide both sides by -6x.
p=\frac{-x^{2}-3y}{-6x}
Dividing by -6x undoes the multiplication by -6x.
p=\frac{x}{6}+\frac{y}{2x}
Divide -x^{2}-3y by -6x.
Examples
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{ 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}