-2(x-6)=4(3-1/2x)

Solution for -2(x-6)=4(3-1/2x) equation:

-2(x-6)=4(3-1/2x)

We move all terms to the left:

-2(x-6)-(4(3-1/2x))=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2(x-6)-(4(-1/2x+3))=0

We multiply parentheses

-2x-(4(-1/2x+3))+12=0

We multiply all the terms by the denominator


-2x*2x+12*2x-1+3))-(4(+3))=0

We add all the numbers together, and all the variables

-2x*2x+12*2x-1+3))-(43)=0

We add all the numbers together, and all the variables

-2x*2x+12*2x=0

Wy multiply elements

-4x^2+24x=0

a = -4; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-4)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-4}=\frac{0}{-8}
=0
$