Solve for b (complex solution)
\left\{\begin{matrix}b=-ax-\frac{c}{x}\text{, }&a\neq 0\text{ and }x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\text{ and }a\neq 0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{bx+c}{x^{2}}\text{, }&\left(c\neq 0\text{ or }b\neq 0\right)\text{ and }\left(b=0\text{ or }x\neq -\frac{c}{b}\right)\text{ and }x\neq 0\text{ and }c\neq -bx\\a\neq 0\text{, }&c=0\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-ax-\frac{c}{x}\text{, }&a\neq 0\text{ and }x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\text{ and }a\neq 0\end{matrix}\right.
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ax^{2}+bx+c=0
Multiply both sides of the equation by a.
bx+c=-ax^{2}
Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.
bx=-ax^{2}-c
Subtract c from both sides.
xb=-ax^{2}-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax-\frac{c}{x}
Divide -ax^{2}-c by x.
ax^{2}+bx+c=0
Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.
ax^{2}+c=-bx
Subtract bx from both sides. Anything subtracted from zero gives its negation.
ax^{2}=-bx-c
Subtract c from both sides.
x^{2}a=-bx-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{bx+c}{x^{2}}
Divide -bx-c by x^{2}.
a=-\frac{bx+c}{x^{2}}\text{, }a\neq 0
Variable a cannot be equal to 0.
ax^{2}+bx+c=0
Multiply both sides of the equation by a.
bx+c=-ax^{2}
Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.
bx=-ax^{2}-c
Subtract c from both sides.
xb=-ax^{2}-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax-\frac{c}{x}
Divide -ax^{2}-c by x.
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}