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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


63x^2/84x^2+48x/84x^2+(-56x)/84x^2+2=0

We multiply all the terms by the denominator


63x^2+48x+(-56x)+2*84x^2=0

Wy multiply elements

63x^2+168x^2+48x+(-56x)=0

We get rid of parentheses

63x^2+168x^2+48x-56x=0

We add all the numbers together, and all the variables

231x^2-8x=0

a = 231; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·231·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*231}=\frac{0}{462}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*231}=\frac{16}{462}
=8/231
$