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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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