x+2=30/x+1

Solution for x+2=30/x+1 equation:

x+2=30/x+1

We move all terms to the left:

x+2-(30/x+1)=0


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

x∈R


We get rid of parentheses

x-30/x-1+2=0

We multiply all the terms by the denominator


x*x-1*x+2*x-30=0

We add all the numbers together, and all the variables

x+x*x-30=0

Wy multiply elements

x^2+x-30=0

a = 1; b = 1; c = -30;
Δ = b2-4ac
Δ = 12-4·1·(-30)
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{-(1)-11}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*1}=\frac{10}{2}
=5
$