1/7x-5=1/2x+1

Solution for 1/7x-5=1/2x+1 equation:

1/7x-5=1/2x+1

We move all terms to the left:

1/7x-5-(1/2x+1)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

1/7x-1/2x-1-5=0

We calculate fractions


2x/14x^2+(-7x)/14x^2-1-5=0

We add all the numbers together, and all the variables

2x/14x^2+(-7x)/14x^2-6=0

We multiply all the terms by the denominator


2x+(-7x)-6*14x^2=0

Wy multiply elements

-84x^2+2x+(-7x)=0

We get rid of parentheses

-84x^2+2x-7x=0

We add all the numbers together, and all the variables

-84x^2-5x=0

a = -84; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-84)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-84}=\frac{0}{-168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-84}=\frac{10}{-168}
=-5/84
$