1-1/2x=5/3x

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

1-1/2x=5/3x

We move all terms to the left:

1-1/2x-(5/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-3x)/6x^2+(-10x)/6x^2+1=0

We multiply all the terms by the denominator


(-3x)+(-10x)+1*6x^2=0

Wy multiply elements

6x^2+(-3x)+(-10x)=0

We get rid of parentheses

6x^2-3x-10x=0

We add all the numbers together, and all the variables

6x^2-13x=0

a = 6; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·6·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*6}=\frac{26}{12}
=2+1/6
$