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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


3x/6x^2+10x/6x^2-4-3=0

We add all the numbers together, and all the variables

3x/6x^2+10x/6x^2-7=0

We multiply all the terms by the denominator


3x+10x-7*6x^2=0

We add all the numbers together, and all the variables

13x-7*6x^2=0

Wy multiply elements

-42x^2+13x=0

a = -42; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-42)·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*-42}=\frac{-26}{-84}
=13/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-42}=\frac{0}{-84}
=0
$