2(x+2)=5/3x+11

Solution for 2(x+2)=5/3x+11 equation:

2(x+2)=5/3x+11

We move all terms to the left:

2(x+2)-(5/3x+11)=0


Domain of the equation: 3x+11)!=0

x∈R


We multiply parentheses

2x-(5/3x+11)+4=0

We get rid of parentheses

2x-5/3x-11+4=0

We multiply all the terms by the denominator


2x*3x-11*3x+4*3x-5=0

Wy multiply elements

6x^2-33x+12x-5=0

We add all the numbers together, and all the variables

6x^2-21x-5=0

a = 6; b = -21; c = -5;
Δ = b2-4ac
Δ = -212-4·6·(-5)
Δ = 561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{561}}{2*6}=\frac{21-\sqrt{561}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{561}}{2*6}=\frac{21+\sqrt{561}}{12}
$