2(1/2x+6)=2(3/2x+11)

Solution for 2(1/2x+6)=2(3/2x+11) equation:

2(1/2x+6)=2(3/2x+11)

We move all terms to the left:

2(1/2x+6)-(2(3/2x+11))=0


Domain of the equation: 2x+6)!=0

x∈R



Domain of the equation: 2x+11))!=0

x∈R


We multiply parentheses

2x-(2(3/2x+11))+12=0

We multiply all the terms by the denominator


2x*2x+12*2x+11))-(2(3+11))=0

We add all the numbers together, and all the variables

2x*2x+12*2x+11))-(214)=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
$