( 1 x - 1 ) d x + ( 3 y + 7 ) d y = 0
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=\frac{\sqrt{-4y\left(3y+7\right)+1}+1}{2}\text{ or }x=\frac{-\sqrt{-4y\left(3y+7\right)+1}+1}{2}\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\left(x=\frac{\sqrt{1-28y-12y^{2}}+1}{2}\text{ or }x=\frac{-\sqrt{1-28y-12y^{2}}+1}{2}\right)\text{ and }y\geq -\frac{\sqrt{13}}{3}-\frac{7}{6}\text{ and }y\leq \frac{\sqrt{13}}{3}-\frac{7}{6}\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=\frac{\sqrt{1-28y-12y^{2}}+1}{2}\text{; }x=\frac{-\sqrt{1-28y-12y^{2}}+1}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{1-28y-12y^{2}}+1}{2}\text{; }x=\frac{-\sqrt{1-28y-12y^{2}}+1}{2}\text{, }&y\geq -\frac{\sqrt{13}}{3}-\frac{7}{6}\text{ and }y\leq \frac{\sqrt{13}}{3}-\frac{7}{6}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.
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\left(1xd-d\right)x+\left(3y+7\right)dy=0
Use the distributive property to multiply 1x-1 by d.
dx^{2}-dx+\left(3y+7\right)dy=0
Use the distributive property to multiply 1xd-d by x.
dx^{2}-dx+\left(3yd+7d\right)y=0
Use the distributive property to multiply 3y+7 by d.
dx^{2}-dx+3dy^{2}+7dy=0
Use the distributive property to multiply 3yd+7d by y.
\left(x^{2}-x+3y^{2}+7y\right)d=0
Combine all terms containing d.
d=0
Divide 0 by x^{2}-x+3y^{2}+7y.
\left(1xd-d\right)x+\left(3y+7\right)dy=0
Use the distributive property to multiply 1x-1 by d.
dx^{2}-dx+\left(3y+7\right)dy=0
Use the distributive property to multiply 1xd-d by x.
dx^{2}-dx+\left(3yd+7d\right)y=0
Use the distributive property to multiply 3y+7 by d.
dx^{2}-dx+3dy^{2}+7dy=0
Use the distributive property to multiply 3yd+7d by y.
\left(x^{2}-x+3y^{2}+7y\right)d=0
Combine all terms containing d.
d=0
Divide 0 by x^{2}-x+3y^{2}+7y.
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}