6/7x-1/5x=23

Solution for 6/7x-1/5x=23 equation:

6/7x-1/5x=23

We move all terms to the left:

6/7x-1/5x-(23)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


30x/35x^2+(-7x)/35x^2-23=0

We multiply all the terms by the denominator


30x+(-7x)-23*35x^2=0

Wy multiply elements

-805x^2+30x+(-7x)=0

We get rid of parentheses

-805x^2+30x-7x=0

We add all the numbers together, and all the variables

-805x^2+23x=0

a = -805; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-805)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-805}=\frac{-46}{-1610}
=1/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-805}=\frac{0}{-1610}
=0
$