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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-3x)/18x^2+(-12x)/18x^2-1+5=0

We add all the numbers together, and all the variables

(-3x)/18x^2+(-12x)/18x^2+4=0

We multiply all the terms by the denominator


(-3x)+(-12x)+4*18x^2=0

Wy multiply elements

72x^2+(-3x)+(-12x)=0

We get rid of parentheses

72x^2-3x-12x=0

We add all the numbers together, and all the variables

72x^2-15x=0

a = 72; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·72·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*72}=\frac{30}{144}
=5/24
$