3/8x-4/3x=5/6

Solution for 3/8x-4/3x=5/6 equation:

3/8x-4/3x=5/6

We move all terms to the left:

3/8x-4/3x-(5/6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x-4/3x-(+5/6)=0

We get rid of parentheses

3/8x-4/3x-5/6=0

We calculate fractions


(-360x^2)/864x^2+324x/864x^2+(-1152x)/864x^2=0

We multiply all the terms by the denominator


(-360x^2)+324x+(-1152x)=0

We get rid of parentheses

-360x^2+324x-1152x=0

We add all the numbers together, and all the variables

-360x^2-828x=0

a = -360; b = -828; c = 0;
Δ = b2-4ac
Δ = -8282-4·(-360)·0
Δ = 685584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{685584}=828$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-828)-828}{2*-360}=\frac{0}{-720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-828)+828}{2*-360}=\frac{1656}{-720}
=-2+3/10
$