1/9x+1/6=1/4x+1

Solution for 1/9x+1/6=1/4x+1 equation:

1/9x+1/6=1/4x+1

We move all terms to the left:

1/9x+1/6-(1/4x+1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

1/9x-1/4x-1+1/6=0

We calculate fractions


144x^2/1296x^2+144x/1296x^2+(-324x)/1296x^2-1=0

We multiply all the terms by the denominator


144x^2+144x+(-324x)-1*1296x^2=0

Wy multiply elements

144x^2-1296x^2+144x+(-324x)=0

We get rid of parentheses

144x^2-1296x^2+144x-324x=0

We add all the numbers together, and all the variables

-1152x^2-180x=0

a = -1152; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-1152)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-1152}=\frac{0}{-2304}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-1152}=\frac{360}{-2304}
=-5/32
$