2/36x+12+3x=22

Solution for 2/36x+12+3x=22 equation:

2/36x+12+3x=22

We move all terms to the left:

2/36x+12+3x-(22)=0


Domain of the equation: 36x!=0

x!=0/36

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/36x-10=0

We multiply all the terms by the denominator


3x*36x-10*36x+2=0

Wy multiply elements

108x^2-360x+2=0

a = 108; b = -360; c = +2;
Δ = b2-4ac
Δ = -3602-4·108·2
Δ = 128736
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:

$\sqrt{\Delta}=\sqrt{128736}=\sqrt{144*894}=\sqrt{144}*\sqrt{894}=12\sqrt{894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-12\sqrt{894}}{2*108}=\frac{360-12\sqrt{894}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+12\sqrt{894}}{2*108}=\frac{360+12\sqrt{894}}{216}
$