Question

(5a-1)(4-x)=(x-2)(2-5x)

Answer 1

Открываем скобки: 5а-4-x=x-4-10x;
5a-x-x+10x=-4-4;
5a+8x=-8;

Answer 2

Let's start by expanding both sides of the equation:

(5a-1)(4-x) = 20a - 5ax - 4 + x (x-2)(2-5x) = -10x^2 + 11x - 4

So we have:

20a - 5ax - 4 + x = -10x^2 + 11x - 4

Now let's simplify this equation by bringing all the terms to one side:

-10x^2 + (11-5a)x + 16 = 0

This is a quadratic equation in x. We can solve it by using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

In this case, a = -10, b = 11-5a, and c = 16. Substituting these values, we get:

x = [(5a-11) ± sqrt((11-5a)^2 - 4(-10)(16))] / (-20)

Simplifying the expression inside the square root, we get:

x = [(5a-11) ± sqrt(25a^2 - 110a + 121)] / (-20)

x = [(5a-11) ± sqrt((5a-11)^2)] / (-20)

x = (5a-11) / (-10) or x = (11-5a) / (-10)

Therefore, the solutions to the equation are:

x = (5a-11) / (-10) or x = (11-5a) / (-10)

We can check these solutions by plugging them back into the original equation.