1/4x-13/12=1-1/6x

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Solution for 1/4x-13/12=1-1/6x equation:



1/4x-13/12=1-1/6x
We move all terms to the left:
1/4x-13/12-(1-1/6x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 6x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/4x-(-1/6x+1)-13/12=0
We get rid of parentheses
1/4x+1/6x-1-13/12=0
We calculate fractions
(-1872x^2)/288x^2+72x/288x^2+48x/288x^2-1=0
We multiply all the terms by the denominator
(-1872x^2)+72x+48x-1*288x^2=0
We add all the numbers together, and all the variables
(-1872x^2)+120x-1*288x^2=0
Wy multiply elements
(-1872x^2)-288x^2+120x=0
We get rid of parentheses
-1872x^2-288x^2+120x=0
We add all the numbers together, and all the variables
-2160x^2+120x=0
a = -2160; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-2160)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-2160}=\frac{-240}{-4320} =1/18 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-2160}=\frac{0}{-4320} =0 $

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