2x+3/x+4=x-1

Solution for 2x+3/x+4=x-1 equation:

2x+3/x+4=x-1

We move all terms to the left:

2x+3/x+4-(x-1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2x+3/x-x+1+4=0

We multiply all the terms by the denominator


2x*x-x*x+1*x+4*x+3=0

We add all the numbers together, and all the variables

5x+2x*x-x*x+3=0

Wy multiply elements

2x^2-1x^2+5x+3=0

We add all the numbers together, and all the variables

x^2+5x+3=0

a = 1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·1·3
Δ = 13
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{-(5)-\sqrt{13}}{2*1}=\frac{-5-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*1}=\frac{-5+\sqrt{13}}{2}
$