3x^2+(2k+1)x+3k-2=0 eching

$$3 x ^ { 2 } + ( 2 k + 1 ) x + 3 k - 2 = 0$$

k uchun yechish

$$k=-\frac{\left(3x-2\right)\left(x+1\right)}{2x+3}$$

$$x\neq -\frac{3}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2k+1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+2kx+x+3k-2=0$$

Ikkala tarafdan 3x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$2kx+x+3k-2=-3x^{2}$$

Ikkala tarafdan x ni ayirish.

$$2kx+3k-2=-3x^{2}-x$$

2 ni ikki tarafga qo’shing.

$$2kx+3k=-3x^{2}-x+2$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x+3\right)k=-3x^{2}-x+2$$

Tenglama standart shaklda.

$$\left(2x+3\right)k=2-x-3x^{2}$$

Ikki tarafini 2x+3 ga bo‘ling.

$$\frac{\left(2x+3\right)k}{2x+3}=-\frac{\left(3x-2\right)\left(x+1\right)}{2x+3}$$

2x+3 ga bo'lish 2x+3 ga ko'paytirishni bekor qiladi.

$$k=-\frac{\left(3x-2\right)\left(x+1\right)}{2x+3}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{4k^{2}-32k+25}}{6}-\frac{k}{3}-\frac{1}{6}$$

$$x=-\frac{\sqrt{4k^{2}-32k+25}}{6}-\frac{k}{3}-\frac{1}{6}$$

x uchun yechish

$$x=\frac{\sqrt{4k^{2}-32k+25}}{6}-\frac{k}{3}-\frac{1}{6}$$

$$x=-\frac{\sqrt{4k^{2}-32k+25}}{6}-\frac{k}{3}-\frac{1}{6}\text{, }k\geq \frac{\sqrt{39}}{2}+4\text{ or }k\leq -\frac{\sqrt{39}}{2}+4$$