x/2x+18-6x=-2

Solution for x/2x+18-6x=-2 equation:

x/2x+18-6x=-2

We move all terms to the left:

x/2x+18-6x-(-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+x/2x+20=0

We multiply all the terms by the denominator


-6x*2x+x+20*2x=0

We add all the numbers together, and all the variables

x-6x*2x+20*2x=0

Wy multiply elements

-12x^2+x+40x=0

We add all the numbers together, and all the variables

-12x^2+41x=0

a = -12; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-12)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-12}=\frac{-82}{-24}
=3+5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-12}=\frac{0}{-24}
=0
$