1/(x+1)=-2x+3

Solution for 1/(x+1)=-2x+3 equation:

1/(x+1)=-2x+3

We move all terms to the left:

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


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

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

x!=-1

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*(x+1)-3*(x+1)+1=0

We multiply parentheses

2x^2+2x-3x-3+1=0

We add all the numbers together, and all the variables

2x^2-1x-2=0

a = 2; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·2·(-2)
Δ = 17
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{-(-1)-\sqrt{17}}{2*2}=\frac{1-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*2}=\frac{1+\sqrt{17}}{4}
$