1/55x=2x+3

Solution for 1/55x=2x+3 equation:

1/55x=2x+3

We move all terms to the left:

1/55x-(2x+3)=0


Domain of the equation: 55x!=0

x!=0/55

x!=0

x∈R


We get rid of parentheses

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}
$