18+x=-3-5/6x

Solution for 18+x=-3-5/6x equation:

18+x=-3-5/6x

We move all terms to the left:

18+x-(-3-5/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-5/6x-3)+18=0

We get rid of parentheses

x+5/6x+3+18=0

We multiply all the terms by the denominator


x*6x+3*6x+18*6x+5=0

Wy multiply elements

6x^2+18x+108x+5=0

We add all the numbers together, and all the variables

6x^2+126x+5=0

a = 6; b = 126; c = +5;
Δ = b2-4ac
Δ = 1262-4·6·5
Δ = 15756
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:

$\sqrt{\Delta}=\sqrt{15756}=\sqrt{4*3939}=\sqrt{4}*\sqrt{3939}=2\sqrt{3939}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{3939}}{2*6}=\frac{-126-2\sqrt{3939}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{3939}}{2*6}=\frac{-126+2\sqrt{3939}}{12}
$