x/14x+1=8x+13

Solution for x/14x+1=8x+13 equation:

x/14x+1=8x+13

We move all terms to the left:

x/14x+1-(8x+13)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We get rid of parentheses

x/14x-8x-13+1=0

We multiply all the terms by the denominator


x-8x*14x-13*14x+1*14x=0

Wy multiply elements

-112x^2+x-182x+14x=0

We add all the numbers together, and all the variables

-112x^2-167x=0

a = -112; b = -167; c = 0;
Δ = b2-4ac
Δ = -1672-4·(-112)·0
Δ = 27889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27889}=167$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-167)-167}{2*-112}=\frac{0}{-224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-167)+167}{2*-112}=\frac{334}{-224}
=-1+55/112
$