15/x=7+9/2x

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

15/x=7+9/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-14x^2+30x-9x=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{-42}{-28}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-14}=\frac{0}{-28}
=0
$