Question

(6x-1)(3-x) = (5-2x)(4+3x).​

Answer 1

х=

$\frac{23}{12}$

Answer 2

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

1. Expand both sides of the equation:

On the left side: (6x-1)(3-x) = 18x^2 - 6x - 3x + 1 = 18x^2 - 9x + 1

On the right side: (5-2x)(4+3x) = 20 - 10x + 15x - 6x^2 = -6x^2 + 5x + 20

So the equation becomes:

18x^2 - 9x + 1 = -6x^2 + 5x + 20

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

18x^2 - 9x + 1 - (-6x^2 + 5x + 20) = 0

Now, combine like terms:

18x^2 - 9x + 1 + 6x^2 - 5x - 20 = 0

3. Combine like terms further:

(18x^2 + 6x^2) + (-9x - 5x) + (1 - 20) = 0

24x^2 - 14x - 19 = 0

4. Now, you have a quadratic equation in the form ax^2 + bx + c = 0, where a = 24, b = -14, and c = -19.

To solve this quadratic equation, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

x = (-(-14) ± √((-14)^2 - 4(24)(-19))) / (2(24))

Simplify the expression inside the square root:

x = (14 ± √(196 + 1824)) / 48 x = (14 ± √2020) / 48

Now, you can simplify the square root further if possible:

x = (14 ± √(4 * 505)) / 48 x = (14 ± 2√505) / 48

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

x = (7 ± √505) / 24

So, the solutions to the equation are:

x = (7 + √505) / 24 and x = (7 - √505) / 24