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

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

d uchun yechish

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafini 2 ga ko‘paytiring.

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

10 olish uchun 5 va 5'ni qo'shing.

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

n-1 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

10+nd-d ga n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

780 hosil qilish uchun 390 va 2 ni ko'paytirish.

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

Ikkala tarafdan 10n ni ayirish.

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

d'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini n^{2}-n ga bo‘ling.

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

n^{2}-n ga bo'lish n^{2}-n ga ko'paytirishni bekor qiladi.

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

780-10n ni n^{2}-n ga bo'lish.

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

n uchun yechish

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