(a+3)x^2-8ax-30=0 eching

$$( a + 3 ) x ^ { 2 } - 8 a x - 30 = 0$$

a uchun yechish

$$a=-\frac{3\left(x^{2}-10\right)}{x\left(x-8\right)}$$

$$x\neq 8\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a+3 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$ax^{2}+3x^{2}-8ax-30=0$$

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

$$ax^{2}-8ax-30=-3x^{2}$$

30 ni ikki tarafga qo’shing.

$$ax^{2}-8ax=-3x^{2}+30$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-8x\right)a=-3x^{2}+30$$

Tenglama standart shaklda.

$$\left(x^{2}-8x\right)a=30-3x^{2}$$

Ikki tarafini x^{2}-8x ga bo‘ling.

$$\frac{\left(x^{2}-8x\right)a}{x^{2}-8x}=\frac{30-3x^{2}}{x^{2}-8x}$$

x^{2}-8x ga bo'lish x^{2}-8x ga ko'paytirishni bekor qiladi.

$$a=\frac{30-3x^{2}}{x^{2}-8x}$$

-3x^{2}+30 ni x^{2}-8x ga bo'lish.

$$a=\frac{3\left(10-x^{2}\right)}{x\left(x-8\right)}$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(8a^{2}+15a+45\right)}+4a}{a+3}\text{; }x=\frac{-\sqrt{2\left(8a^{2}+15a+45\right)}+4a}{a+3}\text{, }&a\neq -3\\x=\frac{5}{4}\text{, }&a=-3\end{matrix}\right,$$