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

Solution for (5)/(x+6)+(2)/(x)=2 equation:

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

We move all terms to the left:

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


Domain of the equation: (x+6)!=0

We move all terms containing x to the left, all other terms to the right

x!=-6

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


5x/(x^2+6x)+(2x+12)/(x^2+6x)-2=0

We multiply all the terms by the denominator


5x+(2x+12)-2*(x^2+6x)=0

We multiply parentheses

-2x^2+5x+(2x+12)-12x=0

We get rid of parentheses

-2x^2+5x+2x-12x+12=0

We add all the numbers together, and all the variables

-2x^2-5x+12=0

a = -2; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-2)·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-2}=\frac{16}{-4}
=-4
$