12/3x+1/6x=11

Solution for 12/3x+1/6x=11 equation:

12/3x+1/6x=11

We move all terms to the left:

12/3x+1/6x-(11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


72x/18x^2+3x/18x^2-11=0

We multiply all the terms by the denominator


72x+3x-11*18x^2=0

We add all the numbers together, and all the variables

75x-11*18x^2=0

Wy multiply elements

-198x^2+75x=0

a = -198; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-198)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-198}=\frac{-150}{-396}
=25/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-198}=\frac{0}{-396}
=0
$