(7)/(x)=(5)/(2x)+27

Solution for (7)/(x)=(5)/(2x)+27 equation:

(7)/(x)=(5)/(2x)+27

We move all terms to the left:

(7)/(x)-((5)/(2x)+27)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+27)!=0

x∈R


We get rid of parentheses

7/x-5/2x-27=0

We calculate fractions


14x/2x^2+(-5x)/2x^2-27=0

We multiply all the terms by the denominator


14x+(-5x)-27*2x^2=0

Wy multiply elements

-54x^2+14x+(-5x)=0

We get rid of parentheses

-54x^2+14x-5x=0

We add all the numbers together, and all the variables

-54x^2+9x=0

a = -54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-54)·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*-54}=\frac{-18}{-108}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-54}=\frac{0}{-108}
=0
$