6(3/2x+1)=-9(1/3x-2)

Solution for 6(3/2x+1)=-9(1/3x-2) equation:

6(3/2x+1)=-9(1/3x-2)

We move all terms to the left:

6(3/2x+1)-(-9(1/3x-2))=0


Domain of the equation: 2x+1)!=0

x∈R



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

x∈R


We multiply parentheses

18x-(-9(1/3x-2))+6=0

We multiply all the terms by the denominator


18x*3x+6*3x-2))-(-9(1-2))=0

We add all the numbers together, and all the variables

18x*3x+6*3x-2))-(-9(-1))=0

We add all the numbers together, and all the variables

18x*3x+6*3x=0

Wy multiply elements

54x^2+18x=0

a = 54; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·54·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*54}=\frac{-36}{108}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*54}=\frac{0}{108}
=0
$