f + \sum I R = 0
Solve for I
\left\{\begin{matrix}I=-\frac{f}{RΣ}\text{, }&R\neq 0\text{ and }Σ\neq 0\\I\in \mathrm{R}\text{, }&\left(R=0\text{ or }Σ=0\right)\text{ and }f=0\end{matrix}\right.
Solve for R
\left\{\begin{matrix}R=-\frac{f}{IΣ}\text{, }&I\neq 0\text{ and }Σ\neq 0\\R\in \mathrm{R}\text{, }&\left(I=0\text{ or }Σ=0\right)\text{ and }f=0\end{matrix}\right.
Share
Copied to clipboard
ΣIR=-f
Subtract f from both sides. Anything subtracted from zero gives its negation.
RΣI=-f
The equation is in standard form.
\frac{RΣI}{RΣ}=-\frac{f}{RΣ}
Divide both sides by ΣR.
I=-\frac{f}{RΣ}
Dividing by ΣR undoes the multiplication by ΣR.
ΣIR=-f
Subtract f from both sides. Anything subtracted from zero gives its negation.
IΣR=-f
The equation is in standard form.
\frac{IΣR}{IΣ}=-\frac{f}{IΣ}
Divide both sides by ΣI.
R=-\frac{f}{IΣ}
Dividing by ΣI undoes the multiplication by ΣI.
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}