8+3/2x=5-2/3x

Solution for 8+3/2x=5-2/3x equation:

8+3/2x=5-2/3x

We move all terms to the left:

8+3/2x-(5-2/3x)=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

3/2x-(-2/3x+5)+8=0

We get rid of parentheses

3/2x+2/3x-5+8=0

We calculate fractions


9x/6x^2+4x/6x^2-5+8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

13x+3*6x^2=0

Wy multiply elements

18x^2+13x=0

a = 18; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·18·0
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*18}=\frac{-26}{36}
=-13/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*18}=\frac{0}{36}
=0
$