-2/3x-3(x+6)+5=-4

Solution for -2/3x-3(x+6)+5=-4 equation:

-2/3x-3(x+6)+5=-4

We move all terms to the left:

-2/3x-3(x+6)+5-(-4)=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+6)+9=0

We multiply parentheses

-2/3x-3x-18+9=0

We multiply all the terms by the denominator


-3x*3x-18*3x+9*3x-2=0

Wy multiply elements

-9x^2-54x+27x-2=0

We add all the numbers together, and all the variables

-9x^2-27x-2=0

a = -9; b = -27; c = -2;
Δ = b2-4ac
Δ = -272-4·(-9)·(-2)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{73}}{2*-9}=\frac{27-3\sqrt{73}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{73}}{2*-9}=\frac{27+3\sqrt{73}}{-18}
$