1/39x+3=3x+1

Solution for 1/39x+3=3x+1 equation:

1/39x+3=3x+1

We move all terms to the left:

1/39x+3-(3x+1)=0


Domain of the equation: 39x!=0

x!=0/39

x!=0

x∈R


We get rid of parentheses

1/39x-3x-1+3=0

We multiply all the terms by the denominator


-3x*39x-1*39x+3*39x+1=0

Wy multiply elements

-117x^2-39x+117x+1=0

We add all the numbers together, and all the variables

-117x^2+78x+1=0

a = -117; b = 78; c = +1;
Δ = b2-4ac
Δ = 782-4·(-117)·1
Δ = 6552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6552}=\sqrt{36*182}=\sqrt{36}*\sqrt{182}=6\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{182}}{2*-117}=\frac{-78-6\sqrt{182}}{-234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{182}}{2*-117}=\frac{-78+6\sqrt{182}}{-234}
$