0,4x+3/7x+6=x

Solution for 0,4x+3/7x+6=x equation:

0.4x+3/7x+6=x

We move all terms to the left:

0.4x+3/7x+6-(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

-0.6x+3/7x+6=0

We multiply all the terms by the denominator


-(0.6x)*7x+6*7x+3=0

We add all the numbers together, and all the variables

-(+0.6x)*7x+6*7x+3=0

We multiply parentheses

-0x^2+6*7x+3=0

Wy multiply elements

-0x^2+42x+3=0

We add all the numbers together, and all the variables

-1x^2+42x+3=0

a = -1; b = 42; c = +3;
Δ = b2-4ac
Δ = 422-4·(-1)·3
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{111}}{2*-1}=\frac{-42-4\sqrt{111}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{111}}{2*-1}=\frac{-42+4\sqrt{111}}{-2}
$