1/7x-16=1/6x+18

Solution for 1/7x-16=1/6x+18 equation:

1/7x-16=1/6x+18

We move all terms to the left:

1/7x-16-(1/6x+18)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 6x+18)!=0

x∈R


We get rid of parentheses

1/7x-1/6x-18-16=0

We calculate fractions


6x/42x^2+(-7x)/42x^2-18-16=0

We add all the numbers together, and all the variables

6x/42x^2+(-7x)/42x^2-34=0

We multiply all the terms by the denominator


6x+(-7x)-34*42x^2=0

Wy multiply elements

-1428x^2+6x+(-7x)=0

We get rid of parentheses

-1428x^2+6x-7x=0

We add all the numbers together, and all the variables

-1428x^2-1x=0

a = -1428; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-1428)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-1428}=\frac{0}{-2856}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-1428}=\frac{2}{-2856}
=-1/1428
$