Question

(x-3)(3x+2)=(5x-4)(x-2)

Answer 1

(x-3)(3x+2)=(5x-4)(x-2)

3x²+2x-9x-6=5x²-10x-4x+8

3x²-7x-6=5x²-14x+8

3x²-7x-6-5x²+14x-8=0

-2x²+7x-14=0 | *(-1)

2x²-7x+14=0

D=b²-4ac=(-7)²-4*2*14=49-112=-63 (D<0 ⇔ решений нет)

Ответ: корней нет.

Answer 2

To solve the equation (x-3)(3x+2) = (5x-4)(x-2), you can follow these steps:

1. Expand both sides of the equation:

   (x-3)(3x+2) = (5x-4)(x-2)

   3x^2 + 2x - 9x - 6 = 5x(x) - 5x(2) - 4(x) + 8

2. Simplify and collect like terms on both sides:

   3x^2 - 7x - 6 = 5x^2 - 10x - 4x + 8

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

   3x^2 - 7x - 6 - 5x^2 + 10x + 4x - 8 = 0

4. Combine like terms:

   (3x^2 - 5x^2) + (-7x + 10x + 4x) + (-6 - 8) = 0

   -2x^2 + 7x - 14 = 0

5. Divide the entire equation by -1 to make it easier to work with:

   2x^2 - 7x + 14 = 0

6. You can now attempt to factor the quadratic equation. However, this quadratic doesn't factor easily into nice integer values. So, you can use the quadratic formula to solve for x:

   The quadratic formula is: x = (-b ± √(b² - 4ac)) / (2a)

   In this equation, a = 2, b = -7, and c = 14.

   x = (-(-7) ± √((-7)² - 4(2)(14))) / (2(2))

   x = (7 ± √(49 - 112)) / 4

   x = (7 ± √(-63)) / 4

7. Since the discriminant (the value inside the square root) is negative, the quadratic equation has complex solutions:

   x = (7 ± √(63)i) / 4

So, the solutions for the equation (x-3)(3x+2) = (5x-4)(x-2) are complex numbers:

x = (7 + √(63)i) / 4 x = (7 - √(63)i) / 4

These are the complex roots of the equation.