9/x+2=7/2x+1

Solution for 9/x+2=7/2x+1 equation:

9/x+2=7/2x+1

We move all terms to the left:

9/x+2-(7/2x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

9/x-7/2x-1+2=0

We calculate fractions


18x/2x^2+(-7x)/2x^2-1+2=0

We add all the numbers together, and all the variables

18x/2x^2+(-7x)/2x^2+1=0

We multiply all the terms by the denominator


18x+(-7x)+1*2x^2=0

Wy multiply elements

2x^2+18x+(-7x)=0

We get rid of parentheses

2x^2+18x-7x=0

We add all the numbers together, and all the variables

2x^2+11x=0

a = 2; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·2·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*2}=\frac{0}{4}
=0
$