nx^2+3x-4=6? eching

$$n x ^ { 2 } + 3 x - 4 = 6 ?$$

n uchun yechish

$$n=-\frac{3x-10}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 3x ni ayirish.

$$nx^{2}-4=6-3x$$

4 ni ikki tarafga qo’shing.

$$nx^{2}=6-3x+4$$

10 olish uchun 6 va 4'ni qo'shing.

$$nx^{2}=10-3x$$

Tenglama standart shaklda.

$$x^{2}n=10-3x$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}n}{x^{2}}=\frac{10-3x}{x^{2}}$$

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

$$n=\frac{10-3x}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{40n+9}-3}{2n}\text{; }x=-\frac{\sqrt{40n+9}+3}{2n}\text{, }&n\neq 0\\x=\frac{10}{3}\text{, }&n=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{40n+9}-3}{2n}\text{; }x=-\frac{\sqrt{40n+9}+3}{2n}\text{, }&n\neq 0\text{ and }n\geq -\frac{9}{40}\\x=\frac{10}{3}\text{, }&n=0\end{matrix}\right,$$