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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+3x^2+3/2*3))-2=0

We multiply all the terms by the denominator


-((+3x^2+3-2*2*3))=0


We calculate terms in parentheses: -((+3x^2+3-2*2*3)), so:

(+3x^2+3-2*2*3)

We get rid of parentheses

3x^2+3-2*2*3

We add all the numbers together, and all the variables

3x^2-9

Back to the equation:

-(3x^2-9)


We get rid of parentheses

-3x^2+9=0

a = -3; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-3)·9
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-3}=\frac{0-6\sqrt{3}}{-6}
=-\frac{6\sqrt{3}}{-6}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-3}=\frac{0+6\sqrt{3}}{-6}
=\frac{6\sqrt{3}}{-6}
=\frac{\sqrt{3}}{-1}
$