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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


(.5x)*3x-8*3x-5*3x-1=0

We add all the numbers together, and all the variables

(+.5x)*3x-8*3x-5*3x-1=0

We multiply parentheses

3x^2-8*3x-5*3x-1=0

Wy multiply elements

3x^2-24x-15x-1=0

We add all the numbers together, and all the variables

3x^2-39x-1=0

a = 3; b = -39; c = -1;
Δ = b2-4ac
Δ = -392-4·3·(-1)
Δ = 1533
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{1533}}{2*3}=\frac{39-\sqrt{1533}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1533}}{2*3}=\frac{39+\sqrt{1533}}{6}
$