4/7x=2/3x-8

Solution for 4/7x=2/3x-8 equation:

4/7x=2/3x-8

We move all terms to the left:

4/7x-(2/3x-8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

4/7x-2/3x+8=0

We calculate fractions


12x/21x^2+(-14x)/21x^2+8=0

We multiply all the terms by the denominator


12x+(-14x)+8*21x^2=0

Wy multiply elements

168x^2+12x+(-14x)=0

We get rid of parentheses

168x^2+12x-14x=0

We add all the numbers together, and all the variables

168x^2-2x=0

a = 168; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·168·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*168}=\frac{4}{336}
=1/84
$