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

Solution for (3x+1/x+4)-(x-2/x-3)=0 equation:

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


Domain of the equation: x+4)!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

7x+3x*x-x*x+3=0

Wy multiply elements

3x^2-1x^2+7x+3=0

We add all the numbers together, and all the variables

2x^2+7x+3=0

a = 2; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·2·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*2}=\frac{-2}{4}
=-1/2
$