x/13x-9x+20=30+2

Solution for x/13x-9x+20=30+2 equation:

x/13x-9x+20=30+2

We move all terms to the left:

x/13x-9x+20-(30+2)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We add all the numbers together, and all the variables

x/13x-9x+20-32=0

We add all the numbers together, and all the variables

-9x+x/13x-12=0

We multiply all the terms by the denominator


-9x*13x+x-12*13x=0

We add all the numbers together, and all the variables

x-9x*13x-12*13x=0

Wy multiply elements

-117x^2+x-156x=0

We add all the numbers together, and all the variables

-117x^2-155x=0

a = -117; b = -155; c = 0;
Δ = b2-4ac
Δ = -1552-4·(-117)·0
Δ = 24025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24025}=155$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-155)-155}{2*-117}=\frac{0}{-234}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+155}{2*-117}=\frac{310}{-234}
=-1+38/117
$