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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


6x/12x^2+(-10x)/12x^2+4-5=0

We add all the numbers together, and all the variables

6x/12x^2+(-10x)/12x^2-1=0

We multiply all the terms by the denominator


6x+(-10x)-1*12x^2=0

Wy multiply elements

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

We get rid of parentheses

-12x^2+6x-10x=0

We add all the numbers together, and all the variables

-12x^2-4x=0

a = -12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-12}=\frac{8}{-24}
=-1/3
$