Solve for m
m=\frac{9y}{x^{2}+x+7}
y\neq 0
Solve for x
x=\frac{3\sqrt{4my-3m^{2}}}{2m}-\frac{1}{2}
x=-\frac{3\sqrt{4my-3m^{2}}}{2m}-\frac{1}{2}\text{, }\left(y\neq 0\text{ and }m=\frac{4y}{3}\right)\text{ or }\left(m\geq \frac{4y}{3}\text{ and }m<0\right)\text{ or }\left(m>0\text{ and }m\leq \frac{4y}{3}\right)
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\left(x^{2}+x+7\right)m=y\times 9
Multiply both sides of the equation by y\left(x^{2}+x+7\right), the least common multiple of y,x^{2}+x+7.
\left(x^{2}+x+7\right)m=9y
The equation is in standard form.
\frac{\left(x^{2}+x+7\right)m}{x^{2}+x+7}=\frac{9y}{x^{2}+x+7}
Divide both sides by x^{2}+x+7.
m=\frac{9y}{x^{2}+x+7}
Dividing by x^{2}+x+7 undoes the multiplication by x^{2}+x+7.
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