सोडोवचें m+5n=m-n/12m

$$m + 5 n = \frac { m - n } { 12 m }$$

n खातीर सोडोवचें

$$n=-\frac{m\left(12m-1\right)}{60m+1}$$

$$m\neq -\frac{1}{60}\text{ and }m\neq 0$$

लिनियर समिकरण सोडोवंक पांवडे

12m वरवीं समिकरणाच्या दोनूय कुशींक गुणाकार करचो.

$$12mm+5n\times 12m=m-n$$

m^{2} मेळोवंक m आनी m गुणचें.

$$12m^{2}+5n\times 12m=m-n$$

60 मेळोवंक 5 आनी 12 गुणचें.

$$12m^{2}+60nm=m-n$$

दोनूय वटांनी n जोडचे.

$$12m^{2}+60nm+n=m$$

दोनूय कुशींतल्यान 12m^{2} वजा करचें.

$$60nm+n=m-12m^{2}$$

n आसपी सगळ्यो संज्ञा एकठांय करच्यो.

$$\left(60m+1\right)n=m-12m^{2}$$

दोनुय कुशींक 60m+1 न भाग लावचो.

$$\frac{\left(60m+1\right)n}{60m+1}=\frac{m\left(1-12m\right)}{60m+1}$$

60m+1 वरवीं भागाकार केल्यार 60m+1 वरवीं केल्लो गुणाकार काडटा.

$$n=\frac{m\left(1-12m\right)}{60m+1}$$

m खातीर सोडोवचें (जटील सोल्यूशन)

$$\left\{\begin{matrix}\\m=\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&\text{unconditionally}\\m=-\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\neq 0\end{matrix}\right.$$

m खातीर सोडोवचें

$$\left\{\begin{matrix}m=-\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\geq \frac{\sqrt{6}}{150}+\frac{7}{300}\text{ or }\left(n\neq 0\text{ and }n\leq -\frac{\sqrt{6}}{150}+\frac{7}{300}\right)\\m=\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\geq \frac{\sqrt{6}}{150}+\frac{7}{300}\text{ or }n\leq -\frac{\sqrt{6}}{150}+\frac{7}{300}\end{matrix}\right.$$