-1/6x+7/2x=5/3

Solution for -1/6x+7/2x=5/3 equation:

-1/6x+7/2x=5/3

We move all terms to the left:

-1/6x+7/2x-(5/3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1/6x+7/2x-(+5/3)=0

We get rid of parentheses

-1/6x+7/2x-5/3=0

We calculate fractions


(-120x^2)/108x^2+(-18x)/108x^2+378x/108x^2=0

We multiply all the terms by the denominator


(-120x^2)+(-18x)+378x=0

We add all the numbers together, and all the variables

(-120x^2)+378x+(-18x)=0

We get rid of parentheses

-120x^2+378x-18x=0

We add all the numbers together, and all the variables

-120x^2+360x=0

a = -120; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·(-120)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*-120}=\frac{-720}{-240}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*-120}=\frac{0}{-240}
=0
$