x/5x+6=2x-2+x

Solution for x/5x+6=2x-2+x equation:

x/5x+6=2x-2+x

We move all terms to the left:

x/5x+6-(2x-2+x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x/5x-(3x-2)+6=0

We get rid of parentheses

x/5x-3x+2+6=0

We multiply all the terms by the denominator


x-3x*5x+2*5x+6*5x=0

Wy multiply elements

-15x^2+x+10x+30x=0

We add all the numbers together, and all the variables

-15x^2+41x=0

a = -15; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-15)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-15}=\frac{-82}{-30}
=2+11/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-15}=\frac{0}{-30}
=0
$