1/5x+1/6x=-33

Solution for 1/5x+1/6x=-33 equation:

1/5x+1/6x=-33

We move all terms to the left:

1/5x+1/6x-(-33)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+1/6x+33=0

We calculate fractions


6x/30x^2+5x/30x^2+33=0

We multiply all the terms by the denominator


6x+5x+33*30x^2=0

We add all the numbers together, and all the variables

11x+33*30x^2=0

Wy multiply elements

990x^2+11x=0

a = 990; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·990·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*990}=\frac{-22}{1980}
=-1/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*990}=\frac{0}{1980}
=0
$