Question

(2(х-1)+3х)/(х-0,4)=х

Answer 1

(2(х-1)+3х)/(х-0,4)=х

$\frac{2(x-1)+3x}{(x-0,4)}=x$

 

$\frac{2x-2+3x}{(x-0,4)}=x$

 

$\frac{5x-2}{(x-0,4)}=x$

 

$x(x-0,4)=5x-2$

 

$x^{2}-0,4x-5x+2=0$

 

$x^{2}-5,4x+2=0$

 

Дальше через дискременант получим

х1 = 5

х2 = 0,4

Answer 2

To solve the equation:

(2(x-1) + 3x)/(x-0.4) = x

Let's simplify the equation step by step:

First, let's expand the numerator:

(2x - 2 + 3x)/(x - 0.4) = x

Combine like terms in the numerator:

5x - 2/(x - 0.4) = x

Next, let's clear the fraction by multiplying both sides of the equation by (x - 0.4):

(x - 0.4)(5x - 2)/(x - 0.4) = x(x - 0.4)

Simplifying:

5x - 2 = x^2 - 0.4x

Rearrange the equation in the standard quadratic form:

x^2 - 0.4x - 5x + 2 = 0

Combine like terms:

x^2 - 5.4x + 2 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation: a = 1, b = -5.4, and c = 2.

Substituting the values:

x = (-(-5.4) ± √((-5.4)^2 - 4(1)(2))) / (2(1))

Simplifying:

x = (5.4 ± √(29.16 - 8)) / 2

x = (5.4 ± √21.16) / 2

x = (5.4 ± 4.6) / 2

x = (5.4 + 4.6) / 2 or x = (5.4 - 4.6) / 2

Solving for x:

x = 10 / 2 or x = 0.8 / 2

x = 5 or x = 0.4

So, the solutions to the equation are x = 5 and x = 0.4.