x/6x-2=-4x+3

Solution for x/6x-2=-4x+3 equation:

x/6x-2=-4x+3

We move all terms to the left:

x/6x-2-(-4x+3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

x/6x+4x-3-2=0

We multiply all the terms by the denominator


x+4x*6x-3*6x-2*6x=0

Wy multiply elements

24x^2+x-18x-12x=0

We add all the numbers together, and all the variables

24x^2-29x=0

a = 24; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·24·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*24}=\frac{58}{48}
=1+5/24
$