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

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## 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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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