4/7x+5x-3x=2x+4-x

Solution for 4/7x+5x-3x=2x+4-x equation:

4/7x+5x-3x=2x+4-x

We move all terms to the left:

4/7x+5x-3x-(2x+4-x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

4/7x+5x-3x-(x+4)=0

We add all the numbers together, and all the variables

2x+4/7x-(x+4)=0

We get rid of parentheses

2x+4/7x-x-4=0

We multiply all the terms by the denominator


2x*7x-x*7x-4*7x+4=0

Wy multiply elements

14x^2-7x^2-28x+4=0

We add all the numbers together, and all the variables

7x^2-28x+4=0

a = 7; b = -28; c = +4;
Δ = b2-4ac
Δ = -282-4·7·4
Δ = 672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{42}}{2*7}=\frac{28-4\sqrt{42}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{42}}{2*7}=\frac{28+4\sqrt{42}}{14}
$