x-5=16/3x+8

Solution for x-5=16/3x+8 equation:

x-5=16/3x+8

We move all terms to the left:

x-5-(16/3x+8)=0


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

x∈R


We get rid of parentheses

x-16/3x-8-5=0

We multiply all the terms by the denominator


x*3x-8*3x-5*3x-16=0

Wy multiply elements

3x^2-24x-15x-16=0

We add all the numbers together, and all the variables

3x^2-39x-16=0

a = 3; b = -39; c = -16;
Δ = b2-4ac
Δ = -392-4·3·(-16)
Δ = 1713
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{1713}}{2*3}=\frac{39-\sqrt{1713}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1713}}{2*3}=\frac{39+\sqrt{1713}}{6}
$