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1/55x=2x+3
We move all terms to the left:
1/55x-(2x+3)=0
Domain of the equation: 55x!=0We get rid of parentheses
x!=0/55
x!=0
x∈R
1/55x-2x-3=0
We multiply all the terms by the denominator
-2x*55x-3*55x+1=0
Wy multiply elements
-110x^2-165x+1=0
a = -110; b = -165; c = +1;
Δ = b2-4ac
Δ = -1652-4·(-110)·1
Δ = 27665
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-\sqrt{27665}}{2*-110}=\frac{165-\sqrt{27665}}{-220} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+\sqrt{27665}}{2*-110}=\frac{165+\sqrt{27665}}{-220} $
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