Solve for m
m=\frac{x^{2}+3x-2}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{17-8m}+3}{2\left(m-1\right)}\text{; }x=\frac{-\sqrt{17-8m}+3}{2\left(m-1\right)}\text{, }&m\neq 1\\x=\frac{2}{3}\text{, }&m=1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{17-8m}+3}{2\left(m-1\right)}\text{; }x=\frac{-\sqrt{17-8m}+3}{2\left(m-1\right)}\text{, }&m\neq 1\text{ and }m\leq \frac{17}{8}\\x=\frac{2}{3}\text{, }&m=1\end{matrix}\right.
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mx^{2}+2=x^{2}+3x
Use the distributive property to multiply x by x+3.
mx^{2}=x^{2}+3x-2
Subtract 2 from both sides.
x^{2}m=x^{2}+3x-2
The equation is in standard form.
\frac{x^{2}m}{x^{2}}=\frac{x^{2}+3x-2}{x^{2}}
Divide both sides by x^{2}.
m=\frac{x^{2}+3x-2}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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