12/3x+x=136

Solution for 12/3x+x=136 equation:

12/3x+x=136

We move all terms to the left:

12/3x+x-(136)=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+12/3x-136=0

We multiply all the terms by the denominator


x*3x-136*3x+12=0

Wy multiply elements

3x^2-408x+12=0

a = 3; b = -408; c = +12;
Δ = b2-4ac
Δ = -4082-4·3·12
Δ = 166320
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:

$\sqrt{\Delta}=\sqrt{166320}=\sqrt{144*1155}=\sqrt{144}*\sqrt{1155}=12\sqrt{1155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-408)-12\sqrt{1155}}{2*3}=\frac{408-12\sqrt{1155}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-408)+12\sqrt{1155}}{2*3}=\frac{408+12\sqrt{1155}}{6}
$