x+3/x-7=-2/x

Solution for x+3/x-7=-2/x equation:

x+3/x-7=-2/x

We move all terms to the left:

x+3/x-7-(-2/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

x+3/x+2/x-7=0

We multiply all the terms by the denominator


x*x-7*x+3+2=0

We add all the numbers together, and all the variables

-7x+x*x+5=0

Wy multiply elements

x^2-7x+5=0

a = 1; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·1·5
Δ = 29
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{-(-7)-\sqrt{29}}{2*1}=\frac{7-\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*1}=\frac{7+\sqrt{29}}{2}
$