-5/6x-4=1/2x

Solution for -5/6x-4=1/2x equation:

-5/6x-4=1/2x

We move all terms to the left:

-5/6x-4-(1/2x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-5/6x-(+1/2x)-4=0

We get rid of parentheses

-5/6x-1/2x-4=0

We calculate fractions


(-10x)/12x^2+(-6x)/12x^2-4=0

We multiply all the terms by the denominator


(-10x)+(-6x)-4*12x^2=0

Wy multiply elements

-48x^2+(-10x)+(-6x)=0

We get rid of parentheses

-48x^2-10x-6x=0

We add all the numbers together, and all the variables

-48x^2-16x=0

a = -48; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-48)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-48}=\frac{32}{-96}
=-1/3
$