2/3x-1/2=-8+1/2x

Solution for 2/3x-1/2=-8+1/2x equation:

2/3x-1/2=-8+1/2x

We move all terms to the left:

2/3x-1/2-(-8+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-8)-1/2=0

We get rid of parentheses

2/3x-1/2x+8-1/2=0

We calculate fractions


16x/24x^2+(-3x)/24x^2+(-3x)/24x^2+8=0

We multiply all the terms by the denominator


16x+(-3x)+(-3x)+8*24x^2=0

Wy multiply elements

192x^2+16x+(-3x)+(-3x)=0

We get rid of parentheses

192x^2+16x-3x-3x=0

We add all the numbers together, and all the variables

192x^2+10x=0

a = 192; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·192·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*192}=\frac{-20}{384}
=-5/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*192}=\frac{0}{384}
=0
$