3x^2-6x+3y-7=0 eching

$$3 x ^ { 2 } - 6 x + 3 y - 7 = 0$$

y uchun yechish

$$y=\frac{7}{3}+2x-x^{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-6x+3y-7=-3x^{2}$$

6x ni ikki tarafga qo’shing.

$$3y-7=-3x^{2}+6x$$

7 ni ikki tarafga qo’shing.

$$3y=-3x^{2}+6x+7$$

Tenglama standart shaklda.

$$3y=7+6x-3x^{2}$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3y}{3}=\frac{7+6x-3x^{2}}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$y=\frac{7+6x-3x^{2}}{3}$$

-3x^{2}+6x+7 ni 3 ga bo'lish.

$$y=\frac{7}{3}+2x-x^{2}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{30-9y}}{3}+1$$

$$x=-\frac{\sqrt{30-9y}}{3}+1$$

x uchun yechish

$$x=\frac{\sqrt{30-9y}}{3}+1$$

$$x=-\frac{\sqrt{30-9y}}{3}+1\text{, }y\leq \frac{10}{3}$$