4/5-2/3x=-1+1/6x

Solution for 4/5-2/3x=-1+1/6x equation:

4/5-2/3x=-1+1/6x

We move all terms to the left:

4/5-2/3x-(-1+1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

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

-2/3x-(1/6x-1)+4/5=0

We get rid of parentheses

-2/3x-1/6x+1+4/5=0

We calculate fractions


432x^2/450x^2+(-300x)/450x^2+(-75x)/450x^2+1=0

We multiply all the terms by the denominator


432x^2+(-300x)+(-75x)+1*450x^2=0

Wy multiply elements

432x^2+450x^2+(-300x)+(-75x)=0

We get rid of parentheses

432x^2+450x^2-300x-75x=0

We add all the numbers together, and all the variables

882x^2-375x=0

a = 882; b = -375; c = 0;
Δ = b2-4ac
Δ = -3752-4·882·0
Δ = 140625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{140625}=375$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-375)-375}{2*882}=\frac{0}{1764}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-375)+375}{2*882}=\frac{750}{1764}
=125/294
$