x+4/x+2-3=5

Solution for x+4/x+2-3=5 equation:

x+4/x+2-3=5

We move all terms to the left:

x+4/x+2-3-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+4/x-6=0

We multiply all the terms by the denominator


x*x-6*x+4=0

We add all the numbers together, and all the variables

-6x+x*x+4=0

Wy multiply elements

x^2-6x+4=0

a = 1; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·1·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*1}=\frac{6-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*1}=\frac{6+2\sqrt{5}}{2}
$