-7+3x=9+2x/x

Solution for -7+3x=9+2x/x equation:

-7+3x=9+2x/x

We move all terms to the left:

-7+3x-(9+2x/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(2x/x+9)-7=0

We get rid of parentheses

3x-2x/x-9-7=0

We multiply all the terms by the denominator


3x*x-2x-9*x-7*x=0

We add all the numbers together, and all the variables

-18x+3x*x=0

Wy multiply elements

3x^2-18x=0

a = 3; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·3·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*3}=\frac{36}{6}
=6
$