-1/3x-8=4x+5

Solution for -1/3x-8=4x+5 equation:

-1/3x-8=4x+5

We move all terms to the left:

-1/3x-8-(4x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x-4x-5-8=0

We multiply all the terms by the denominator


-4x*3x-5*3x-8*3x-1=0

Wy multiply elements

-12x^2-15x-24x-1=0

We add all the numbers together, and all the variables

-12x^2-39x-1=0

a = -12; b = -39; c = -1;
Δ = b2-4ac
Δ = -392-4·(-12)·(-1)
Δ = 1473
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{-(-39)-\sqrt{1473}}{2*-12}=\frac{39-\sqrt{1473}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1473}}{2*-12}=\frac{39+\sqrt{1473}}{-24}
$