x^2+(3a-4)x-12a=0 eching

$$x ^ { 2 } + ( 3 a - 4 ) x - 12 a = 0$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}\\a=-\frac{x}{3}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=4\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3a-4 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+3ax-4x-12a=0$$

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3ax-4x-12a=-x^{2}$$

4x ni ikki tarafga qo’shing.

$$3ax-12a=-x^{2}+4x$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3x-12\right)a=-x^{2}+4x$$

Tenglama standart shaklda.

$$\left(3x-12\right)a=4x-x^{2}$$

Ikki tarafini 3x-12 ga bo‘ling.

$$\frac{\left(3x-12\right)a}{3x-12}=\frac{x\left(4-x\right)}{3x-12}$$

3x-12 ga bo'lish 3x-12 ga ko'paytirishni bekor qiladi.

$$a=\frac{x\left(4-x\right)}{3x-12}$$

x\left(4-x\right) ni 3x-12 ga bo'lish.

$$a=-\frac{x}{3}$$

a uchun yechish

$$\left\{\begin{matrix}\\a=-\frac{x}{3}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=4\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3a-4 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+3ax-4x-12a=0$$

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3ax-4x-12a=-x^{2}$$

4x ni ikki tarafga qo’shing.

$$3ax-12a=-x^{2}+4x$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3x-12\right)a=-x^{2}+4x$$

Tenglama standart shaklda.

$$\left(3x-12\right)a=4x-x^{2}$$

Ikki tarafini 3x-12 ga bo‘ling.

$$\frac{\left(3x-12\right)a}{3x-12}=\frac{x\left(4-x\right)}{3x-12}$$

3x-12 ga bo'lish 3x-12 ga ko'paytirishni bekor qiladi.

$$a=\frac{x\left(4-x\right)}{3x-12}$$

x\left(4-x\right) ni 3x-12 ga bo'lish.

$$a=-\frac{x}{3}$$

x uchun yechish

$$x=-3a$$

$$x=4$$