-1/2x-6=-4+1.5x

Solution for -1/2x-6=-4+1.5x equation:

-1/2x-6=-4+1.5x

We move all terms to the left:

-1/2x-6-(-4+1.5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(1.5x-4)-6=0

We get rid of parentheses

-1/2x-1.5x+4-6=0

We multiply all the terms by the denominator


-(1.5x)*2x+4*2x-6*2x-1=0

We add all the numbers together, and all the variables

-(+1.5x)*2x+4*2x-6*2x-1=0

We multiply parentheses

-2x^2+4*2x-6*2x-1=0

Wy multiply elements

-2x^2+8x-12x-1=0

We add all the numbers together, and all the variables

-2x^2-4x-1=0

a = -2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·(-2)·(-1)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{2}}{2*-2}=\frac{4-2\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{2}}{2*-2}=\frac{4+2\sqrt{2}}{-4}
$