5/6x=2/7x-4

Solution for 5/6x=2/7x-4 equation:

5/6x=2/7x-4

We move all terms to the left:

5/6x-(2/7x-4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 7x-4)!=0

x∈R


We get rid of parentheses

5/6x-2/7x+4=0

We calculate fractions


35x/42x^2+(-12x)/42x^2+4=0

We multiply all the terms by the denominator


35x+(-12x)+4*42x^2=0

Wy multiply elements

168x^2+35x+(-12x)=0

We get rid of parentheses

168x^2+35x-12x=0

We add all the numbers together, and all the variables

168x^2+23x=0

a = 168; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·168·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*168}=\frac{-46}{336}
=-23/168
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*168}=\frac{0}{336}
=0
$