7+9/2x=15/x

Solution for 7+9/2x=15/x equation:

7+9/2x=15/x

We move all terms to the left:

7+9/2x-(15/x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-(+15/x)+7=0

We get rid of parentheses

9/2x-15/x+7=0

We calculate fractions


9x/2x^2+(-30x)/2x^2+7=0

We multiply all the terms by the denominator


9x+(-30x)+7*2x^2=0

Wy multiply elements

14x^2+9x+(-30x)=0

We get rid of parentheses

14x^2+9x-30x=0

We add all the numbers together, and all the variables

14x^2-21x=0

a = 14; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·14·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*14}=\frac{42}{28}
=1+1/2
$