Solve for a
a=-\frac{1}{10}+\frac{196}{5n}
n\neq 0
Solve for n
n=\frac{392}{10a+1}
a\neq -\frac{1}{10}
Share
Copied to clipboard
10an=390-\left(n-1-1\right)
Multiply both sides of the equation by 10.
10an=390-\left(n-2\right)
Subtract 1 from -1 to get -2.
10an=390-n+2
To find the opposite of n-2, find the opposite of each term.
10an=392-n
Add 390 and 2 to get 392.
10na=392-n
The equation is in standard form.
\frac{10na}{10n}=\frac{392-n}{10n}
Divide both sides by 10n.
a=\frac{392-n}{10n}
Dividing by 10n undoes the multiplication by 10n.
a=-\frac{1}{10}+\frac{196}{5n}
Divide 392-n by 10n.
10an=390-\left(n-1-1\right)
Multiply both sides of the equation by 10.
10an=390-\left(n-2\right)
Subtract 1 from -1 to get -2.
10an=390-n+2
To find the opposite of n-2, find the opposite of each term.
10an=392-n
Add 390 and 2 to get 392.
10an+n=392
Add n to both sides.
\left(10a+1\right)n=392
Combine all terms containing n.
\frac{\left(10a+1\right)n}{10a+1}=\frac{392}{10a+1}
Divide both sides by 10a+1.
n=\frac{392}{10a+1}
Dividing by 10a+1 undoes the multiplication by 10a+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}