Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{by}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&\left(b=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{ax^{2}}{y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&\left(a=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{by}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&\left(b=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{ax^{2}}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.
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ax^{2}=-by
Subtract by from both sides. Anything subtracted from zero gives its negation.
x^{2}a=-by
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=-\frac{by}{x^{2}}
Divide both sides by x^{2}.
a=-\frac{by}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
by=-ax^{2}
Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.
yb=-ax^{2}
The equation is in standard form.
\frac{yb}{y}=-\frac{ax^{2}}{y}
Divide both sides by y.
b=-\frac{ax^{2}}{y}
Dividing by y undoes the multiplication by y.
ax^{2}=-by
Subtract by from both sides. Anything subtracted from zero gives its negation.
x^{2}a=-by
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=-\frac{by}{x^{2}}
Divide both sides by x^{2}.
a=-\frac{by}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
by=-ax^{2}
Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.
yb=-ax^{2}
The equation is in standard form.
\frac{yb}{y}=-\frac{ax^{2}}{y}
Divide both sides by y.
b=-\frac{ax^{2}}{y}
Dividing by y undoes the multiplication by y.
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
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Matrix
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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}