Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{x^{2}-6}{2b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&\left(x=\sqrt{6}\text{ or }x=-\sqrt{6}\right)\text{ and }b=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{x^{2}-6}{2a}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&\left(x=\sqrt{6}\text{ or }x=-\sqrt{6}\right)\text{ and }a=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{x^{2}-6}{2b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }|x|=\sqrt{6}\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{x^{2}-6}{2a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&a=0\text{ and }|x|=\sqrt{6}\end{matrix}\right.
Graph
Share
Copied to clipboard
-2ab=6-x^{2}
Subtract x^{2} from both sides.
\left(-2b\right)a=6-x^{2}
The equation is in standard form.
\frac{\left(-2b\right)a}{-2b}=\frac{6-x^{2}}{-2b}
Divide both sides by -2b.
a=\frac{6-x^{2}}{-2b}
Dividing by -2b undoes the multiplication by -2b.
a=-\frac{6-x^{2}}{2b}
Divide -x^{2}+6 by -2b.
-2ab=6-x^{2}
Subtract x^{2} from both sides.
\left(-2a\right)b=6-x^{2}
The equation is in standard form.
\frac{\left(-2a\right)b}{-2a}=\frac{6-x^{2}}{-2a}
Divide both sides by -2a.
b=\frac{6-x^{2}}{-2a}
Dividing by -2a undoes the multiplication by -2a.
b=-\frac{6-x^{2}}{2a}
Divide -x^{2}+6 by -2a.
-2ab=6-x^{2}
Subtract x^{2} from both sides.
\left(-2b\right)a=6-x^{2}
The equation is in standard form.
\frac{\left(-2b\right)a}{-2b}=\frac{6-x^{2}}{-2b}
Divide both sides by -2b.
a=\frac{6-x^{2}}{-2b}
Dividing by -2b undoes the multiplication by -2b.
a=-\frac{6-x^{2}}{2b}
Divide 6-x^{2} by -2b.
-2ab=6-x^{2}
Subtract x^{2} from both sides.
\left(-2a\right)b=6-x^{2}
The equation is in standard form.
\frac{\left(-2a\right)b}{-2a}=\frac{6-x^{2}}{-2a}
Divide both sides by -2a.
b=\frac{6-x^{2}}{-2a}
Dividing by -2a undoes the multiplication by -2a.
b=-\frac{6-x^{2}}{2a}
Divide 6-x^{2} by -2a.
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}