5х(3х-2)-15х(4+х)=140

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вопрос

Let's solve the equation step by step:

5(3x-2) - 15x(4+x) = 140

First, distribute the 5 and the -15x:

15x - 10 - 60x - 15x^2 = 140

Combine like terms:

-45x - 10 - 15x^2 = 140

Rearrange the equation to set it equal to 0:

-15x^2 - 45x - 150 = 0

Divide the entire equation by -15 to simplify:

x^2 + 3x + 10 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 3, and c = 10. Plug these values into the formula:

x = (-(3) ± √(3^2 - 4(1)(10))) / 2(1)
x = (-3 ± √(9 - 40)) / 2
x = (-3 ± √(-31)) / 2

Since we have a negative value inside the square root, the solutions are complex numbers:

x = (-3 ± √31i) / 2

Therefore, the solutions to the equation are x = (-3 + √31i) / 2 and x = (-3 - √31i) / 2.