(2x+1)/x+(x-7)/6=2

Solution for (2x+1)/x+(x-7)/6=2 equation:

(2x+1)/x+(x-7)/6=2

We move all terms to the left:

(2x+1)/x+(x-7)/6-(2)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


(12x+6)/6x+(x^2-7x)/6x-2=0

We multiply all the terms by the denominator


(12x+6)+(x^2-7x)-2*6x=0

Wy multiply elements

(12x+6)+(x^2-7x)-12x=0

We get rid of parentheses

x^2+12x-7x-12x+6=0

We add all the numbers together, and all the variables

x^2-7x+6=0

a = 1; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*1}=\frac{12}{2}
=6
$