12+1/5x=18+1/7x

Solution for 12+1/5x=18+1/7x equation:

12+1/5x=18+1/7x

We move all terms to the left:

12+1/5x-(18+1/7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(1/7x+18)+12=0

We get rid of parentheses

1/5x-1/7x-18+12=0

We calculate fractions


7x/35x^2+(-5x)/35x^2-18+12=0

We add all the numbers together, and all the variables

7x/35x^2+(-5x)/35x^2-6=0

We multiply all the terms by the denominator


7x+(-5x)-6*35x^2=0

Wy multiply elements

-210x^2+7x+(-5x)=0

We get rid of parentheses

-210x^2+7x-5x=0

We add all the numbers together, and all the variables

-210x^2+2x=0

a = -210; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-210)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-210}=\frac{-4}{-420}
=1/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-210}=\frac{0}{-420}
=0
$