3/8x=1/3x+3

Solution for 3/8x=1/3x+3 equation:

3/8x=1/3x+3

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


9x/24x^2+(-8x)/24x^2-3=0

We multiply all the terms by the denominator


9x+(-8x)-3*24x^2=0

Wy multiply elements

-72x^2+9x+(-8x)=0

We get rid of parentheses

-72x^2+9x-8x=0

We add all the numbers together, and all the variables

-72x^2+x=0

a = -72; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-72)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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