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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-x/3x+5-5/6-6/5=0

We calculate fractions


x+(-150x)/450x+(-375x)/450x+(-648x)/450x+5=0

We multiply all the terms by the denominator


x*450x+(-150x)+(-375x)+(-648x)+5*450x=0

Wy multiply elements

450x^2+(-150x)+(-375x)+(-648x)+2250x=0

We get rid of parentheses

450x^2-150x-375x-648x+2250x=0

We add all the numbers together, and all the variables

450x^2+1077x=0

a = 450; b = 1077; c = 0;
Δ = b2-4ac
Δ = 10772-4·450·0
Δ = 1159929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1159929}=1077$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1077)-1077}{2*450}=\frac{-2154}{900}
=-2+59/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1077)+1077}{2*450}=\frac{0}{900}
=0
$