2/3x=3/8x+6

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

2/3x=3/8x+6

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x+6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


16x/24x^2+(-9x)/24x^2-6=0

We multiply all the terms by the denominator


16x+(-9x)-6*24x^2=0

Wy multiply elements

-144x^2+16x+(-9x)=0

We get rid of parentheses

-144x^2+16x-9x=0

We add all the numbers together, and all the variables

-144x^2+7x=0

a = -144; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-144)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-144}=\frac{-14}{-288}
=7/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-144}=\frac{0}{-288}
=0
$