y=4ac-b^2/4a eching

$$y = \frac { 4 a c - b ^ { 2 } } { 4 a }$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{b^{2}}{4\left(y-c\right)}\text{, }&b\neq 0\text{ and }y\neq c\\a\neq 0\text{, }&b=0\text{ and }y=c\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4a ga ko'paytirish.

$$y\times 4a=4ac-b^{2}$$

Ikkala tarafdan 4ac ni ayirish.

$$y\times 4a-4ac=-b^{2}$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(y\times 4-4c\right)a=-b^{2}$$

Tenglama standart shaklda.

$$\left(4y-4c\right)a=-b^{2}$$

Ikki tarafini 4y-4c ga bo‘ling.

$$\frac{\left(4y-4c\right)a}{4y-4c}=-\frac{b^{2}}{4y-4c}$$

4y-4c ga bo'lish 4y-4c ga ko'paytirishni bekor qiladi.

$$a=-\frac{b^{2}}{4y-4c}$$

-b^{2} ni 4y-4c ga bo'lish.

$$a=-\frac{b^{2}}{4\left(y-c\right)}$$

a qiymati 0 teng bo‘lmaydi.

$$a=-\frac{b^{2}}{4\left(y-c\right)}\text{, }a\neq 0$$

b uchun yechish (complex solution)

$$b=-2\sqrt{a}\sqrt{c-y}$$

$$b=2\sqrt{a}\sqrt{c-y}\text{, }a\neq 0$$

b uchun yechish

$$b=2\sqrt{a\left(c-y\right)}$$

$$b=-2\sqrt{a\left(c-y\right)}\text{, }\left(a<0\text{ or }y\leq c\right)\text{ and }\left(a>0\text{ or }y\geq c\right)\text{ and }a\neq 0$$