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

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

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

We move all terms to the left:

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


Domain of the equation: 3)x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


((-1-2x*3)x)-9*3)x)-5*3)x)=0


We calculate terms in parentheses: +((-1-2x*3)x), so:

(-1-2x*3)x

We add all the numbers together, and all the variables

(-2x*3-1)x

We multiply parentheses

-6x^2-1x

Back to the equation:

+(-6x^2-1x)


Wy multiply elements

(-6x^2-1x)-81x^2=0

We get rid of parentheses

-6x^2-81x^2-1x=0

We add all the numbers together, and all the variables

-87x^2-1x=0

a = -87; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-87)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-87}=\frac{0}{-174}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-87}=\frac{2}{-174}
=-1/87
$