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1/2x-1/4=9/36x-1

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Solution for 1/2x-1/4=9/36x-1 equation:



1/2x-1/4=9/36x-1
We move all terms to the left:
1/2x-1/4-(9/36x-1)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 36x-1)!=0
x∈R
We get rid of parentheses
1/2x-9/36x+1-1/4=0
We calculate fractions
(-216x^2)/1152x^2+576x/1152x^2+(-288x)/1152x^2+1=0
We multiply all the terms by the denominator
(-216x^2)+576x+(-288x)+1*1152x^2=0
Wy multiply elements
(-216x^2)+1152x^2+576x+(-288x)=0
We get rid of parentheses
-216x^2+1152x^2+576x-288x=0
We add all the numbers together, and all the variables
936x^2+288x=0
a = 936; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·936·0
Δ = 82944
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{82944}=288
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*936}=\frac{-576}{1872} =-4/13
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*936}=\frac{0}{1872} =0

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