x+5=2/1x+1

Solution for x+5=2/1x+1 equation:

x+5=2/1x+1

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

x^2-1x+5x-2=0

We add all the numbers together, and all the variables

x^2+4x-2=0

a = 1; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·1·(-2)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*1}=\frac{-4-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*1}=\frac{-4+2\sqrt{6}}{2}
$