27-1/2x=1/7x+9

Solution for 27-1/2x=1/7x+9 equation:

27-1/2x=1/7x+9

We move all terms to the left:

27-1/2x-(1/7x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x+9)!=0

x∈R


We get rid of parentheses

-1/2x-1/7x-9+27=0

We calculate fractions


(-7x)/14x^2+(-2x)/14x^2-9+27=0

We add all the numbers together, and all the variables

(-7x)/14x^2+(-2x)/14x^2+18=0

We multiply all the terms by the denominator


(-7x)+(-2x)+18*14x^2=0

Wy multiply elements

252x^2+(-7x)+(-2x)=0

We get rid of parentheses

252x^2-7x-2x=0

We add all the numbers together, and all the variables

252x^2-9x=0

a = 252; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·252·0
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*252}=\frac{0}{504}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*252}=\frac{18}{504}
=1/28
$