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 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^2-87x+1=0

a = 6; b = -87; c = +1;
Δ = b2-4ac
Δ = -872-4·6·1
Δ = 7545
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{-(-87)-\sqrt{7545}}{2*6}=\frac{87-\sqrt{7545}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+\sqrt{7545}}{2*6}=\frac{87+\sqrt{7545}}{12}
$