1/6x+3/2x=14

Solution for 1/6x+3/2x=14 equation:

1/6x+3/2x=14

We move all terms to the left:

1/6x+3/2x-(14)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


2x/12x^2+18x/12x^2-14=0

We multiply all the terms by the denominator


2x+18x-14*12x^2=0

We add all the numbers together, and all the variables

20x-14*12x^2=0

Wy multiply elements

-168x^2+20x=0

a = -168; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-168)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-168}=\frac{-40}{-336}
=5/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-168}=\frac{0}{-336}
=0
$