1/7x-1/6x=3/4

Solution for 1/7x-1/6x=3/4 equation:

1/7x-1/6x=3/4

We move all terms to the left:

1/7x-1/6x-(3/4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-1/6x-(+3/4)=0

We get rid of parentheses

1/7x-1/6x-3/4=0

We calculate fractions


(-756x^2)/672x^2+96x/672x^2+(-112x)/672x^2=0

We multiply all the terms by the denominator


(-756x^2)+96x+(-112x)=0

We get rid of parentheses

-756x^2+96x-112x=0

We add all the numbers together, and all the variables

-756x^2-16x=0

a = -756; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-756)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-756}=\frac{0}{-1512}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-756}=\frac{32}{-1512}
=-4/189
$