-2x-6=(3/2)(-2x-2)

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

-2x-6=(3/2)(-2x-2)

We move all terms to the left:

-2x-6-((3/2)(-2x-2))=0


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((-6x^2+3/2*-2))-2x-6=0

We multiply all the terms by the denominator


-((-6x^2+3-2x*2*-2))-6*2*-2))=0


We calculate terms in parentheses: -((-6x^2+3-2x*2*-2)), so:

(-6x^2+3-2x*2*-2)

We get rid of parentheses

-6x^2-2x*2*+3-2

We add all the numbers together, and all the variables

-6x^2-2x*2*+1

Wy multiply elements

-6x^2-4x^2+1

We add all the numbers together, and all the variables

-10x^2+1

Back to the equation:

-(-10x^2+1)


We add all the numbers together, and all the variables

-(-10x^2+1)=0

We get rid of parentheses

10x^2-1=0

a = 10; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·10·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*10}=\frac{0-2\sqrt{10}}{20}
=-\frac{2\sqrt{10}}{20}
=-\frac{\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*10}=\frac{0+2\sqrt{10}}{20}
=\frac{2\sqrt{10}}{20}
=\frac{\sqrt{10}}{10}
$