Solve for n
n=-\frac{3x-10}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{40n+9}-3}{2n}\text{; }x=-\frac{\sqrt{40n+9}+3}{2n}\text{, }&n\neq 0\\x=\frac{10}{3}\text{, }&n=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{40n+9}-3}{2n}\text{; }x=-\frac{\sqrt{40n+9}+3}{2n}\text{, }&n\neq 0\text{ and }n\geq -\frac{9}{40}\\x=\frac{10}{3}\text{, }&n=0\end{matrix}\right.
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nx^{2}-4=6-3x
Subtract 3x from both sides.
nx^{2}=6-3x+4
Add 4 to both sides.
nx^{2}=10-3x
Add 6 and 4 to get 10.
x^{2}n=10-3x
The equation is in standard form.
\frac{x^{2}n}{x^{2}}=\frac{10-3x}{x^{2}}
Divide both sides by x^{2}.
n=\frac{10-3x}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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