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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-15x)/18x^2+(-6x)/18x^2+5+2=0

We add all the numbers together, and all the variables

(-15x)/18x^2+(-6x)/18x^2+7=0

We multiply all the terms by the denominator


(-15x)+(-6x)+7*18x^2=0

Wy multiply elements

126x^2+(-15x)+(-6x)=0

We get rid of parentheses

126x^2-15x-6x=0

We add all the numbers together, and all the variables

126x^2-21x=0

a = 126; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·126·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*126}=\frac{0}{252}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*126}=\frac{42}{252}
=1/6
$