7/x+9=5/2x+

Solution for 7/x+9=5/2x+ equation:

7/x+9=5/2x+

We move all terms to the left:

7/x+9-(5/2x+)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

7/x-(+5/2x)+9=0

We get rid of parentheses

7/x-5/2x+9=0

We calculate fractions


14x/2x^2+(-5x)/2x^2+9=0

We multiply all the terms by the denominator


14x+(-5x)+9*2x^2=0

Wy multiply elements

18x^2+14x+(-5x)=0

We get rid of parentheses

18x^2+14x-5x=0

We add all the numbers together, and all the variables

18x^2+9x=0

a = 18; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·18·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*18}=\frac{-18}{36}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*18}=\frac{0}{36}
=0
$