-2/5x+1/6=-3/4x=5/3

Solution for -2/5x+1/6=-3/4x=5/3 equation:

-2/5x+1/6=-3/4x=5/3

We move all terms to the left:

-2/5x+1/6-(-3/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-2/5x+3/4x+1/6=0

We calculate fractions


80x^2/720x^2+(-288x)/720x^2+540x/720x^2=0

We multiply all the terms by the denominator


80x^2+(-288x)+540x=0

We add all the numbers together, and all the variables

80x^2+540x+(-288x)=0

We get rid of parentheses

80x^2+540x-288x=0

We add all the numbers together, and all the variables

80x^2+252x=0

a = 80; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·80·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*80}=\frac{-504}{160}
=-3+3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*80}=\frac{0}{160}
=0
$