-1/3x+5=7+5/6x

Solution for -1/3x+5=7+5/6x equation:

-1/3x+5=7+5/6x

We move all terms to the left:

-1/3x+5-(7+5/6x)=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

-1/3x-(5/6x+7)+5=0

We get rid of parentheses

-1/3x-5/6x-7+5=0

We calculate fractions


(-6x)/18x^2+(-15x)/18x^2-7+5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-36x^2+(-6x)+(-15x)=0

We get rid of parentheses

-36x^2-6x-15x=0

We add all the numbers together, and all the variables

-36x^2-21x=0

a = -36; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-36)·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*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-36}=\frac{42}{-72}
=-7/12
$