2x+1=5/(x+2

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

2x+1=5/(x+2

We move all terms to the left:

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


Domain of the equation: (x+2)+1!=0

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

(x+2)!=-1

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*(x+2)=0

We multiply parentheses

2x^2+4x=0

a = 2; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·2·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*2}=\frac{0}{4}
=0
$