7-1/6x=10/3x

Solution for 7-1/6x=10/3x equation:

7-1/6x=10/3x

We move all terms to the left:

7-1/6x-(10/3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/6x-(+10/3x)+7=0

We get rid of parentheses

-1/6x-10/3x+7=0

We calculate fractions


(-3x)/18x^2+(-60x)/18x^2+7=0

We multiply all the terms by the denominator


(-3x)+(-60x)+7*18x^2=0

Wy multiply elements

126x^2+(-3x)+(-60x)=0

We get rid of parentheses

126x^2-3x-60x=0

We add all the numbers together, and all the variables

126x^2-63x=0

a = 126; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·126·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*126}=\frac{0}{252}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*126}=\frac{126}{252}
=1/2
$