Issolvi left(5+5+left(n-1right)dright)n/2=390

$$\frac{ \left( 5+5+ \left( n-1 \right) d \right) n }{ 2 } =390$$

Solvi għal d

$$d=-\frac{10\left(n-78\right)}{n\left(n-1\right)}$$

$$n\neq 1\text{ and }n\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat b'2.

$$\left(5+5+\left(n-1\right)d\right)n=390\times 2$$

Żid 5 u 5 biex tikseb 10.

$$\left(10+\left(n-1\right)d\right)n=390\times 2$$

Uża l-propjetà distributtiva biex timmultiplika n-1 b'd.

$$\left(10+nd-d\right)n=390\times 2$$

Uża l-propjetà distributtiva biex timmultiplika 10+nd-d b'n.

$$10n+dn^{2}-dn=390\times 2$$

Immultiplika 390 u 2 biex tikseb 780.

$$10n+dn^{2}-dn=780$$

Naqqas 10n miż-żewġ naħat.

$$dn^{2}-dn=780-10n$$

Ikkombina t-termini kollha li fihom d.

$$\left(n^{2}-n\right)d=780-10n$$

Iddividi ż-żewġ naħat b'n^{2}-n.

$$\frac{\left(n^{2}-n\right)d}{n^{2}-n}=\frac{780-10n}{n^{2}-n}$$

Meta tiddividi b'n^{2}-n titneħħa l-multiplikazzjoni b'n^{2}-n.

$$d=\frac{780-10n}{n^{2}-n}$$

Iddividi 780-10n b'n^{2}-n.

$$d=\frac{10\left(78-n\right)}{n\left(n-1\right)}$$

Solvi għal n

$$\left\{\begin{matrix}n=\frac{\sqrt{d^{2}+3100d+100}+d-10}{2d}\text{; }n=\frac{-\sqrt{d^{2}+3100d+100}+d-10}{2d}\text{, }&d\leq -20\sqrt{6006}-1550\text{ or }\left(d\neq 0\text{ and }d\geq 20\sqrt{6006}-1550\right)\\n=78\text{, }&d=0\end{matrix}\right.$$