2/7x-1/2x=3/4+2

Solution for 2/7x-1/2x=3/4+2 equation:

2/7x-1/2x=3/4+2

We move all terms to the left:

2/7x-1/2x-(3/4+2)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

2/7x-1/2x-2-3/4=0

We calculate fractions


(-84x^2)/224x^2+64x/224x^2+(-112x)/224x^2-2=0

We multiply all the terms by the denominator


(-84x^2)+64x+(-112x)-2*224x^2=0

Wy multiply elements

(-84x^2)-448x^2+64x+(-112x)=0

We get rid of parentheses

-84x^2-448x^2+64x-112x=0

We add all the numbers together, and all the variables

-532x^2-48x=0

a = -532; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-532)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-532}=\frac{0}{-1064}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-532}=\frac{96}{-1064}
=-12/133
$