Solve for k (complex solution)
\left\{\begin{matrix}k=-\frac{3x^{2}-y}{1-x}\text{, }&x\neq 1\\k\in \mathrm{C}\text{, }&y=3\text{ and }x=1\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=-\frac{3x^{2}-y}{1-x}\text{, }&x\neq 1\\k\in \mathrm{R}\text{, }&y=3\text{ and }x=1\end{matrix}\right.
Solve for x (complex solution)
x=\frac{\sqrt{12y+k^{2}-12k}+k}{6}
x=\frac{-\sqrt{12y+k^{2}-12k}+k}{6}
Solve for x
x=\frac{\sqrt{12y+k^{2}-12k}+k}{6}
x=\frac{-\sqrt{12y+k^{2}-12k}+k}{6}\text{, }y\geq -\frac{k^{2}}{12}+k
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3x^{2}-kx+k=y
Swap sides so that all variable terms are on the left hand side.
-kx+k=y-3x^{2}
Subtract 3x^{2} from both sides.
\left(-x+1\right)k=y-3x^{2}
Combine all terms containing k.
\left(1-x\right)k=y-3x^{2}
The equation is in standard form.
\frac{\left(1-x\right)k}{1-x}=\frac{y-3x^{2}}{1-x}
Divide both sides by -x+1.
k=\frac{y-3x^{2}}{1-x}
Dividing by -x+1 undoes the multiplication by -x+1.
3x^{2}-kx+k=y
Swap sides so that all variable terms are on the left hand side.
-kx+k=y-3x^{2}
Subtract 3x^{2} from both sides.
\left(-x+1\right)k=y-3x^{2}
Combine all terms containing k.
\left(1-x\right)k=y-3x^{2}
The equation is in standard form.
\frac{\left(1-x\right)k}{1-x}=\frac{y-3x^{2}}{1-x}
Divide both sides by -x+1.
k=\frac{y-3x^{2}}{1-x}
Dividing by -x+1 undoes the multiplication by -x+1.
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}