2+1/6x=3/8x-1

Solution for 2+1/6x=3/8x-1 equation:

2+1/6x=3/8x-1

We move all terms to the left:

2+1/6x-(3/8x-1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x-1)!=0

x∈R


We get rid of parentheses

1/6x-3/8x+1+2=0

We calculate fractions


8x/48x^2+(-18x)/48x^2+1+2=0

We add all the numbers together, and all the variables

8x/48x^2+(-18x)/48x^2+3=0

We multiply all the terms by the denominator


8x+(-18x)+3*48x^2=0

Wy multiply elements

144x^2+8x+(-18x)=0

We get rid of parentheses

144x^2+8x-18x=0

We add all the numbers together, and all the variables

144x^2-10x=0

a = 144; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·144·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*144}=\frac{0}{288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*144}=\frac{20}{288}
=5/72
$