4x-8=30+5/6x

Solution for 4x-8=30+5/6x equation:

4x-8=30+5/6x

We move all terms to the left:

4x-8-(30+5/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(5/6x+30)-8=0

We get rid of parentheses

4x-5/6x-30-8=0

We multiply all the terms by the denominator


4x*6x-30*6x-8*6x-5=0

Wy multiply elements

24x^2-180x-48x-5=0

We add all the numbers together, and all the variables

24x^2-228x-5=0

a = 24; b = -228; c = -5;
Δ = b2-4ac
Δ = -2282-4·24·(-5)
Δ = 52464
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:

$\sqrt{\Delta}=\sqrt{52464}=\sqrt{16*3279}=\sqrt{16}*\sqrt{3279}=4\sqrt{3279}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-4\sqrt{3279}}{2*24}=\frac{228-4\sqrt{3279}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+4\sqrt{3279}}{2*24}=\frac{228+4\sqrt{3279}}{48}
$