(b-4)x^2+(2b-8)x+15=0? eching

$$( b - 4 ) x ^ { 2 } + ( 2 b - 8 ) x + 15 = 0 ?$$

b uchun yechish

$$b=-\frac{15-8x-4x^{2}}{x\left(x+2\right)}$$

$$x\neq -2\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

b-4 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$bx^{2}-4x^{2}+\left(2b-8\right)x+15=0$$

2b-8 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$bx^{2}-4x^{2}+2bx-8x+15=0$$

4x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$bx^{2}+2bx-8x+15=4x^{2}$$

8x ni ikki tarafga qo’shing.

$$bx^{2}+2bx+15=4x^{2}+8x$$

Ikkala tarafdan 15 ni ayirish.

$$bx^{2}+2bx=4x^{2}+8x-15$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}+2x\right)b=4x^{2}+8x-15$$

Ikki tarafini x^{2}+2x ga bo‘ling.

$$\frac{\left(x^{2}+2x\right)b}{x^{2}+2x}=\frac{4x^{2}+8x-15}{x^{2}+2x}$$

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

$$b=\frac{4x^{2}+8x-15}{x^{2}+2x}$$

4x^{2}+8x-15 ni x^{2}+2x ga bo'lish.

$$b=\frac{4x^{2}+8x-15}{x\left(x+2\right)}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{\left(b-19\right)\left(b-4\right)}-b+4}{b-4}$$

$$x=\frac{-\sqrt{\left(b-19\right)\left(b-4\right)}-b+4}{b-4}\text{, }b\neq 4$$

x uchun yechish

$$x=\frac{\sqrt{\left(b-19\right)\left(b-4\right)}-b+4}{b-4}$$

$$x=\frac{-\sqrt{\left(b-19\right)\left(b-4\right)}-b+4}{b-4}\text{, }b\geq 19\text{ or }b<4$$