Question

(6у+2)(5-у)=47-(2у-3)(3у-1)

Answer 1

(6у+2)(5-у)=47-(2у-3)(3у-1)

30у-6у2+10-2у=47-(6у2-2у-9у+3)

-6у2+28у+10=44-6у2+11у

-6у2+28у+10-44+6у2-11у=0

17у-34=0

17у=34

у=2

Answer 2

To solve the given equation, let's simplify both sides step by step:

Starting with the left side of the equation: (6у + 2)(5 - у) = 47

Expanding the left side using the distributive property: 30у - 6у^2 + 10 - 2у = 47

Combining like terms: 30у - 6у^2 - 2у + 10 = 47

Simplifying further: -6у^2 + 28у + 10 = 47

Now let's simplify the right side of the equation: (2у - 3)(3у - 1) = 47

Expanding the right side using the distributive property: 6у^2 - 2у - 9у + 3 = 47

Combining like terms: 6у^2 - 11у + 3 = 47

Moving all terms to one side of the equation: 6у^2 - 11у + 3 - 47 = 0

Simplifying further: 6у^2 - 11у - 44 = 0

Now we have the equation: -6у^2 + 28у + 10 = 6у^2 - 11у - 44

To solve this equation, we can move all terms to one side: -12у^2 + 39у + 54 = 0

However, this quadratic equation cannot be easily factored. We can solve it using the quadratic formula:

у = (-b ± √(b^2 - 4ac)) / (2a)

For the equation -12у^2 + 39у + 54 = 0, the coefficients are: a = -12 b = 39 c = 54

Substituting these values into the quadratic formula: у = (-(39) ± √((39)^2 - 4(-12)(54))) / (2(-12))

Simplifying the formula: у = (-39 ± √(1521 + 2592)) / (-24) у = (-39 ± √4113) / (-24)

Thus, the solutions for the quadratic equation are: у ≈ 3.63 у ≈ -1.05

Please note that these are approximate values rounded to two decimal places.