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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

4x/6x^2+3x/6x^2-9=0

We multiply all the terms by the denominator


4x+3x-9*6x^2=0

We add all the numbers together, and all the variables

7x-9*6x^2=0

Wy multiply elements

-54x^2+7x=0

a = -54; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-54)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-54}=\frac{-14}{-108}
=7/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-54}=\frac{0}{-108}
=0
$