(5x+1/5x+1)+2x=-2

Solution for (5x+1/5x+1)+2x=-2 equation:

(5x+1/5x+1)+2x=-2

We move all terms to the left:

(5x+1/5x+1)+2x-(-2)=0


Domain of the equation: 5x+1)!=0

x∈R


We add all the numbers together, and all the variables

2x+(5x+1/5x+1)+2=0

We get rid of parentheses

2x+5x+1/5x+1+2=0

We multiply all the terms by the denominator


2x*5x+5x*5x+1*5x+2*5x+1=0

Wy multiply elements

10x^2+25x^2+5x+10x+1=0

We add all the numbers together, and all the variables

35x^2+15x+1=0

a = 35; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·35·1
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{85}}{2*35}=\frac{-15-\sqrt{85}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{85}}{2*35}=\frac{-15+\sqrt{85}}{70}
$