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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-112x^2)/112x^2+32x/112x^2+(-84x)/112x^2-1=0

We multiply all the terms by the denominator


(-112x^2)+32x+(-84x)-1*112x^2=0

Wy multiply elements

(-112x^2)-112x^2+32x+(-84x)=0

We get rid of parentheses

-112x^2-112x^2+32x-84x=0

We add all the numbers together, and all the variables

-224x^2-52x=0

a = -224; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·(-224)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*-224}=\frac{0}{-448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*-224}=\frac{104}{-448}
=-13/56
$