1/3x+9=-5-2/5x

Solution for 1/3x+9=-5-2/5x equation:

1/3x+9=-5-2/5x

We move all terms to the left:

1/3x+9-(-5-2/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-2/5x-5)+9=0

We get rid of parentheses

1/3x+2/5x+5+9=0

We calculate fractions


5x/15x^2+6x/15x^2+5+9=0

We add all the numbers together, and all the variables

5x/15x^2+6x/15x^2+14=0

We multiply all the terms by the denominator


5x+6x+14*15x^2=0

We add all the numbers together, and all the variables

11x+14*15x^2=0

Wy multiply elements

210x^2+11x=0

a = 210; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·210·0
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*210}=\frac{-22}{420}
=-11/210
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*210}=\frac{0}{420}
=0
$