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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/24x^2+(-8x)/24x^2+9x/24x^2+5=0

We multiply all the terms by the denominator


3x+(-8x)+9x+5*24x^2=0

We add all the numbers together, and all the variables

12x+(-8x)+5*24x^2=0

Wy multiply elements

120x^2+12x+(-8x)=0

We get rid of parentheses

120x^2+12x-8x=0

We add all the numbers together, and all the variables

120x^2+4x=0

a = 120; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·120·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*120}=\frac{-8}{240}
=-1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*120}=\frac{0}{240}
=0
$