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7/5x-1/3=1/6x-18

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Solution for 7/5x-1/3=1/6x-18 equation:



7/5x-1/3=1/6x-18
We move all terms to the left:
7/5x-1/3-(1/6x-18)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 6x-18)!=0
x∈R
We get rid of parentheses
7/5x-1/6x+18-1/3=0
We calculate fractions
(-180x^2)/270x^2+378x/270x^2+(-45x)/270x^2+18=0
We multiply all the terms by the denominator
(-180x^2)+378x+(-45x)+18*270x^2=0
Wy multiply elements
(-180x^2)+4860x^2+378x+(-45x)=0
We get rid of parentheses
-180x^2+4860x^2+378x-45x=0
We add all the numbers together, and all the variables
4680x^2+333x=0
a = 4680; b = 333; c = 0;
Δ = b2-4ac
Δ = 3332-4·4680·0
Δ = 110889
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{110889}=333
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(333)-333}{2*4680}=\frac{-666}{9360} =-37/520
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(333)+333}{2*4680}=\frac{0}{9360} =0

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