3+1/7x=1+1/2x

Solution for 3+1/7x=1+1/2x equation:

3+1/7x=1+1/2x

We move all terms to the left:

3+1/7x-(1+1/2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-(1/2x+1)+3=0

We get rid of parentheses

1/7x-1/2x-1+3=0

We calculate fractions


2x/14x^2+(-7x)/14x^2-1+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

28x^2+2x+(-7x)=0

We get rid of parentheses

28x^2+2x-7x=0

We add all the numbers together, and all the variables

28x^2-5x=0

a = 28; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·28·0
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*28}=\frac{0}{56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*28}=\frac{10}{56}
=5/28
$