x+1/3x+8=-12

Solution for x+1/3x+8=-12 equation:

x+1/3x+8=-12

We move all terms to the left:

x+1/3x+8-(-12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/3x+20=0

We multiply all the terms by the denominator


x*3x+20*3x+1=0

Wy multiply elements

3x^2+60x+1=0

a = 3; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·3·1
Δ = 3588
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:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{897}}{2*3}=\frac{-60-2\sqrt{897}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{897}}{2*3}=\frac{-60+2\sqrt{897}}{6}
$