14x-13=1/3x+1

Solution for 14x-13=1/3x+1 equation:

14x-13=1/3x+1

We move all terms to the left:

14x-13-(1/3x+1)=0


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

x∈R


We get rid of parentheses

14x-1/3x-1-13=0

We multiply all the terms by the denominator


14x*3x-1*3x-13*3x-1=0

Wy multiply elements

42x^2-3x-39x-1=0

We add all the numbers together, and all the variables

42x^2-42x-1=0

a = 42; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·42·(-1)
Δ = 1932
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:

$\sqrt{\Delta}=\sqrt{1932}=\sqrt{4*483}=\sqrt{4}*\sqrt{483}=2\sqrt{483}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{483}}{2*42}=\frac{42-2\sqrt{483}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{483}}{2*42}=\frac{42+2\sqrt{483}}{84}
$