2/3x+28+3(x-11)=50

Solution for 2/3x+28+3(x-11)=50 equation:

2/3x+28+3(x-11)=50

We move all terms to the left:

2/3x+28+3(x-11)-(50)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+3(x-11)-22=0

We multiply parentheses

2/3x+3x-33-22=0

We multiply all the terms by the denominator


3x*3x-33*3x-22*3x+2=0

Wy multiply elements

9x^2-99x-66x+2=0

We add all the numbers together, and all the variables

9x^2-165x+2=0

a = 9; b = -165; c = +2;
Δ = b2-4ac
Δ = -1652-4·9·2
Δ = 27153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27153}=\sqrt{9*3017}=\sqrt{9}*\sqrt{3017}=3\sqrt{3017}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-3\sqrt{3017}}{2*9}=\frac{165-3\sqrt{3017}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+3\sqrt{3017}}{2*9}=\frac{165+3\sqrt{3017}}{18}
$