-8+2/3x+19=2x-5-x

Solution for -8+2/3x+19=2x-5-x equation:

-8+2/3x+19=2x-5-x

We move all terms to the left:

-8+2/3x+19-(2x-5-x)=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-(x-5)-8+19=0

We add all the numbers together, and all the variables

2/3x-(x-5)+11=0

We get rid of parentheses

2/3x-x+5+11=0

We multiply all the terms by the denominator


-x*3x+5*3x+11*3x+2=0

Wy multiply elements

-3x^2+15x+33x+2=0

We add all the numbers together, and all the variables

-3x^2+48x+2=0

a = -3; b = 48; c = +2;
Δ = b2-4ac
Δ = 482-4·(-3)·2
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{582}}{2*-3}=\frac{-48-2\sqrt{582}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{582}}{2*-3}=\frac{-48+2\sqrt{582}}{-6}
$