x+3/x+7+2/x+5=-1

Solution for x+3/x+7+2/x+5=-1 equation:

x+3/x+7+2/x+5=-1

We move all terms to the left:

x+3/x+7+2/x+5-(-1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x+2/x+13=0

We multiply all the terms by the denominator


x*x+13*x+3+2=0

We add all the numbers together, and all the variables

13x+x*x+5=0

Wy multiply elements

x^2+13x+5=0

a = 1; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·1·5
Δ = 149
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{-(13)-\sqrt{149}}{2*1}=\frac{-13-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{149}}{2*1}=\frac{-13+\sqrt{149}}{2}
$