2x+7=3(4+2/3x)

Solution for 2x+7=3(4+2/3x) equation:

2x+7=3(4+2/3x)

We move all terms to the left:

2x+7-(3(4+2/3x))=0


Domain of the equation: 3x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(3(2/3x+4))+7=0

We multiply all the terms by the denominator


2x*3x+7*3x+4))-(3(2+4))=0

We add all the numbers together, and all the variables

2x*3x+7*3x+4))-(36)=0

We add all the numbers together, and all the variables

2x*3x+7*3x=0

Wy multiply elements

6x^2+21x=0

a = 6; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·6·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*6}=\frac{0}{12}
=0
$