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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-18x-24x-2=0

We add all the numbers together, and all the variables

-9x^2-42x-2=0

a = -9; b = -42; c = -2;
Δ = b2-4ac
Δ = -422-4·(-9)·(-2)
Δ = 1692
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:

$\sqrt{\Delta}=\sqrt{1692}=\sqrt{36*47}=\sqrt{36}*\sqrt{47}=6\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{47}}{2*-9}=\frac{42-6\sqrt{47}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{47}}{2*-9}=\frac{42+6\sqrt{47}}{-18}
$