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

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

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

We move all terms to the left:

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


Domain of the equation: 3x-2)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+6x+3x-8=0

We add all the numbers together, and all the variables

3x^2+9x-8=0

a = 3; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·3·(-8)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{177}}{2*3}=\frac{-9-\sqrt{177}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{177}}{2*3}=\frac{-9+\sqrt{177}}{6}
$