2(x/3-5)+1/3x=-19

Solution for 2(x/3-5)+1/3x=-19 equation:

2(x/3-5)+1/3x=-19

We move all terms to the left:

2(x/3-5)+1/3x-(-19)=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(x/3-5)+1/3x+19=0

We multiply parentheses

2x+1/3x-10+19=0

We multiply all the terms by the denominator


2x*3x-10*3x+19*3x+1=0

Wy multiply elements

6x^2-30x+57x+1=0

We add all the numbers together, and all the variables

6x^2+27x+1=0

a = 6; b = 27; c = +1;
Δ = b2-4ac
Δ = 272-4·6·1
Δ = 705
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{-(27)-\sqrt{705}}{2*6}=\frac{-27-\sqrt{705}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{705}}{2*6}=\frac{-27+\sqrt{705}}{12}
$