4+1/3x=-48-8x

Solution for 4+1/3x=-48-8x equation:

4+1/3x=-48-8x

We move all terms to the left:

4+1/3x-(-48-8x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-8x-48)+4=0

We get rid of parentheses

1/3x+8x+48+4=0

We multiply all the terms by the denominator


8x*3x+48*3x+4*3x+1=0

Wy multiply elements

24x^2+144x+12x+1=0

We add all the numbers together, and all the variables

24x^2+156x+1=0

a = 24; b = 156; c = +1;
Δ = b2-4ac
Δ = 1562-4·24·1
Δ = 24240
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:

$\sqrt{\Delta}=\sqrt{24240}=\sqrt{16*1515}=\sqrt{16}*\sqrt{1515}=4\sqrt{1515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-4\sqrt{1515}}{2*24}=\frac{-156-4\sqrt{1515}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+4\sqrt{1515}}{2*24}=\frac{-156+4\sqrt{1515}}{48}
$