1/5x-7-4/10x+1=1/7

Solution for 1/5x-7-4/10x+1=1/7 equation:

1/5x-7-4/10x+1=1/7

We move all terms to the left:

1/5x-7-4/10x+1-(1/7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-4/10x-7+1-(+1/7)=0

We add all the numbers together, and all the variables

1/5x-4/10x-6-(+1/7)=0

We get rid of parentheses

1/5x-4/10x-6-1/7=0

We calculate fractions


(-50x^2)/2450x^2+490x/2450x^2+(-980x)/2450x^2-6=0

We multiply all the terms by the denominator


(-50x^2)+490x+(-980x)-6*2450x^2=0

Wy multiply elements

(-50x^2)-14700x^2+490x+(-980x)=0

We get rid of parentheses

-50x^2-14700x^2+490x-980x=0

We add all the numbers together, and all the variables

-14750x^2-490x=0

a = -14750; b = -490; c = 0;
Δ = b2-4ac
Δ = -4902-4·(-14750)·0
Δ = 240100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{240100}=490$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-490)-490}{2*-14750}=\frac{0}{-29500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-490)+490}{2*-14750}=\frac{980}{-29500}
=-49/1475
$