3(2x+1)+2/2x+1=9

Solution for 3(2x+1)+2/2x+1=9 equation:

3(2x+1)+2/2x+1=9

We move all terms to the left:

3(2x+1)+2/2x+1-(9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

6x+2/2x+3-8=0

We multiply all the terms by the denominator


6x*2x+3*2x-8*2x+2=0

Wy multiply elements

12x^2+6x-16x+2=0

We add all the numbers together, and all the variables

12x^2-10x+2=0

a = 12; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·12·2
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*12}=\frac{8}{24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*12}=\frac{12}{24}
=1/2
$