3/8x=2/3x-1

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

3/8x=2/3x-1

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


9x/24x^2+(-16x)/24x^2+1=0

We multiply all the terms by the denominator


9x+(-16x)+1*24x^2=0

Wy multiply elements

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

We get rid of parentheses

24x^2+9x-16x=0

We add all the numbers together, and all the variables

24x^2-7x=0

a = 24; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·24·0
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*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*24}=\frac{14}{48}
=7/24
$