Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{b\left(x+c\right)}{4c}\text{, }&c\neq 0\\a\in \mathrm{C}\text{, }&\left(b=0\text{ or }x=0\right)\text{ and }c=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{4ac}{x+c}\text{, }&c\neq -x\\b\in \mathrm{C}\text{, }&\left(a=0\text{ and }c=-x\right)\text{ or }\left(c=0\text{ and }x=0\right)\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{b\left(x+c\right)}{4c}\text{, }&c\neq 0\\a\in \mathrm{R}\text{, }&\left(b=0\text{ or }x=0\right)\text{ and }c=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{4ac}{x+c}\text{, }&c\neq -x\\b\in \mathrm{R}\text{, }&\left(a=0\text{ and }c=-x\right)\text{ or }\left(c=0\text{ and }x=0\right)\end{matrix}\right.
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4ac=bx+bc
Use the distributive property to multiply b by x+c.
4ca=bx+bc
The equation is in standard form.
\frac{4ca}{4c}=\frac{b\left(x+c\right)}{4c}
Divide both sides by 4c.
a=\frac{b\left(x+c\right)}{4c}
Dividing by 4c undoes the multiplication by 4c.
4ac=bx+bc
Use the distributive property to multiply b by x+c.
bx+bc=4ac
Swap sides so that all variable terms are on the left hand side.
\left(x+c\right)b=4ac
Combine all terms containing b.
\frac{\left(x+c\right)b}{x+c}=\frac{4ac}{x+c}
Divide both sides by x+c.
b=\frac{4ac}{x+c}
Dividing by x+c undoes the multiplication by x+c.
4ac=bx+bc
Use the distributive property to multiply b by x+c.
4ca=bx+bc
The equation is in standard form.
\frac{4ca}{4c}=\frac{b\left(x+c\right)}{4c}
Divide both sides by 4c.
a=\frac{b\left(x+c\right)}{4c}
Dividing by 4c undoes the multiplication by 4c.
4ac=bx+bc
Use the distributive property to multiply b by x+c.
bx+bc=4ac
Swap sides so that all variable terms are on the left hand side.
\left(x+c\right)b=4ac
Combine all terms containing b.
\frac{\left(x+c\right)b}{x+c}=\frac{4ac}{x+c}
Divide both sides by x+c.
b=\frac{4ac}{x+c}
Dividing by x+c undoes the multiplication by x+c.
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}