2/7x=1/2x+4

Solution for 2/7x=1/2x+4 equation:

2/7x=1/2x+4

We move all terms to the left:

2/7x-(1/2x+4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

2/7x-1/2x-4=0

We calculate fractions


4x/14x^2+(-7x)/14x^2-4=0

We multiply all the terms by the denominator


4x+(-7x)-4*14x^2=0

Wy multiply elements

-56x^2+4x+(-7x)=0

We get rid of parentheses

-56x^2+4x-7x=0

We add all the numbers together, and all the variables

-56x^2-3x=0

a = -56; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-56)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-56}=\frac{0}{-112}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-56}=\frac{6}{-112}
=-3/56
$