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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


9x/24x^2+16x/24x^2+9x/24x^2-8=0

We multiply all the terms by the denominator


9x+16x+9x-8*24x^2=0

We add all the numbers together, and all the variables

34x-8*24x^2=0

Wy multiply elements

-192x^2+34x=0

a = -192; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-192)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-192}=\frac{-68}{-384}
=17/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-192}=\frac{0}{-384}
=0
$