4(x+3)=8(1/2x+1)

Solution for 4(x+3)=8(1/2x+1) equation:

4(x+3)=8(1/2x+1)

We move all terms to the left:

4(x+3)-(8(1/2x+1))=0


Domain of the equation: 2x+1))!=0

x∈R


We multiply parentheses

4x-(8(1/2x+1))+12=0

We multiply all the terms by the denominator


4x*2x+12*2x+1))-(8(1+1))=0

We add all the numbers together, and all the variables

4x*2x+12*2x+1))-(82)=0

We add all the numbers together, and all the variables

4x*2x+12*2x=0

Wy multiply elements

8x^2+24x=0

a = 8; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·8·0
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*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*8}=\frac{0}{16}
=0
$