Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{2bx}{5\left(b-3x\right)}\text{, }&x\neq \frac{b}{3}\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{15ax}{5a-2x}\text{, }&a\neq \frac{2x}{5}\\b\in \mathrm{C}\text{, }&x=0\text{ and }a=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{2bx}{5\left(b-3x\right)}\text{, }&x\neq \frac{b}{3}\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{15ax}{5a-2x}\text{, }&a\neq \frac{2x}{5}\\b\in \mathrm{R}\text{, }&x=0\text{ and }a=0\end{matrix}\right.
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-15ax+5ab=2bx
Add 5ab to both sides.
\left(-15x+5b\right)a=2bx
Combine all terms containing a.
\left(5b-15x\right)a=2bx
The equation is in standard form.
\frac{\left(5b-15x\right)a}{5b-15x}=\frac{2bx}{5b-15x}
Divide both sides by -15x+5b.
a=\frac{2bx}{5b-15x}
Dividing by -15x+5b undoes the multiplication by -15x+5b.
a=\frac{2bx}{5\left(b-3x\right)}
Divide 2bx by -15x+5b.
2bx-5ab=-15ax
Swap sides so that all variable terms are on the left hand side.
\left(2x-5a\right)b=-15ax
Combine all terms containing b.
\frac{\left(2x-5a\right)b}{2x-5a}=-\frac{15ax}{2x-5a}
Divide both sides by 2x-5a.
b=-\frac{15ax}{2x-5a}
Dividing by 2x-5a undoes the multiplication by 2x-5a.
-15ax+5ab=2bx
Add 5ab to both sides.
\left(-15x+5b\right)a=2bx
Combine all terms containing a.
\left(5b-15x\right)a=2bx
The equation is in standard form.
\frac{\left(5b-15x\right)a}{5b-15x}=\frac{2bx}{5b-15x}
Divide both sides by -15x+5b.
a=\frac{2bx}{5b-15x}
Dividing by -15x+5b undoes the multiplication by -15x+5b.
a=\frac{2bx}{5\left(b-3x\right)}
Divide 2bx by -15x+5b.
2bx-5ab=-15ax
Swap sides so that all variable terms are on the left hand side.
\left(2x-5a\right)b=-15ax
Combine all terms containing b.
\frac{\left(2x-5a\right)b}{2x-5a}=-\frac{15ax}{2x-5a}
Divide both sides by 2x-5a.
b=-\frac{15ax}{2x-5a}
Dividing by 2x-5a undoes the multiplication by 2x-5a.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}