11/3x+1/6x=36

Solution for 11/3x+1/6x=36 equation:

11/3x+1/6x=36

We move all terms to the left:

11/3x+1/6x-(36)=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


66x/18x^2+3x/18x^2-36=0

We multiply all the terms by the denominator


66x+3x-36*18x^2=0

We add all the numbers together, and all the variables

69x-36*18x^2=0

Wy multiply elements

-648x^2+69x=0

a = -648; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·(-648)·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*-648}=\frac{-138}{-1296}
=23/216
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*-648}=\frac{0}{-1296}
=0
$