Question

(3x-1) (7х+5)-(2x+3) (6x+1) =4

Answer 1

Ответ:

-2/3; 2

Объяснение:

(3х - 1)(7х + 5) - (2х + 3)(6х + 1) = 4

(21х² + 15х - 7х - 5) - (12х² + 2х + 18х + 3) = 4

(21х² + 8х - 5) - (12х² + 20х + 3) = 4

21х² + 8х - 5 - 12х² - 20х - 3 - 4 = 0

9х² - 12х - 12 = 0

а = 9; в = -12; с = -12

Д = в² - 4ас

Д = (-12)² - 4 * 9 * (-12) = 144 + 432 = 576

√Д = √576 = 24

х1 = (-в - √Д)/2а

х1 = (12 - 24)/(2*9) = -12/18 = -2/3

х2 = (-в + √Д)/2а

х2 = (12 + 24)/(2*9) = 36/18 = 2

Answer 2

To solve the equation (3x-1)(7x+5) - (2x+3)(6x+1) = 4, follow these steps:

1. Expand both sides of the equation:

(3x-1)(7x+5) - (2x+3)(6x+1) = 4

Expanding the left side:

(21x^2 + 15x - 7x - 5) - (12x^2 + 2x - 18x - 3) = 4

Now simplify the equation:

21x^2 + 15x - 7x - 5 - 12x^2 - 2x + 18x + 3 = 4

2. Combine like terms:

(21x^2 - 12x^2) + (15x - 7x - 2x + 18x) + (-5 + 3) = 4

9x^2 + 24x - 2 = 4

3. Move all terms to one side of the equation to set it equal to zero:

9x^2 + 24x - 2 - 4 = 0

9x^2 + 24x - 6 = 0

4. Divide the entire equation by the greatest common divisor to simplify it:

3(3x^2 + 8x - 2) = 0

5. Now, you can solve the quadratic equation 3x^2 + 8x - 2 = 0 using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = 8, and c = -2. Plug these values into the formula:

x = (-8 ± √(8^2 - 4 * 3 * (-2))) / (2 * 3)

x = (-8 ± √(64 + 24)) / 6

x = (-8 ± √88) / 6

x = (-8 ± 2√22) / 6

Now, you can simplify further by dividing both the numerator and denominator by 2:

x = (-4 ± √22) / 3

So, the solutions to the equation (3x-1)(7x+5) - (2x+3)(6x+1) = 4 are:

x = (-4 + √22) / 3 x = (-4 - √22) / 3

These are the two solutions for the given equation.