12x+8/3x+1=-72

Solution for 12x+8/3x+1=-72 equation:

12x+8/3x+1=-72

We move all terms to the left:

12x+8/3x+1-(-72)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

12x+8/3x+73=0

We multiply all the terms by the denominator


12x*3x+73*3x+8=0

Wy multiply elements

36x^2+219x+8=0

a = 36; b = 219; c = +8;
Δ = b2-4ac
Δ = 2192-4·36·8
Δ = 46809
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:

$\sqrt{\Delta}=\sqrt{46809}=\sqrt{9*5201}=\sqrt{9}*\sqrt{5201}=3\sqrt{5201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(219)-3\sqrt{5201}}{2*36}=\frac{-219-3\sqrt{5201}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(219)+3\sqrt{5201}}{2*36}=\frac{-219+3\sqrt{5201}}{72}
$