13x+2=1/3x-1

Solution for 13x+2=1/3x-1 equation:

13x+2=1/3x-1

We move all terms to the left:

13x+2-(1/3x-1)=0


Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

13x-1/3x+1+2=0

We multiply all the terms by the denominator


13x*3x+1*3x+2*3x-1=0

Wy multiply elements

39x^2+3x+6x-1=0

We add all the numbers together, and all the variables

39x^2+9x-1=0

a = 39; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·39·(-1)
Δ = 237
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{-(9)-\sqrt{237}}{2*39}=\frac{-9-\sqrt{237}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{237}}{2*39}=\frac{-9+\sqrt{237}}{78}
$