x-2/x=3/x-4

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

x-2/x=3/x-4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4x+x*x-5=0

Wy multiply elements

x^2+4x-5=0

a = 1; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*1}=\frac{2}{2}
=1
$