x/12.9x+10=34+9.9x

Solution for x/12.9x+10=34+9.9x equation:

x/12.9x+10=34+9.9x

We move all terms to the left:

x/12.9x+10-(34+9.9x)=0


Domain of the equation: 12.9x!=0

x!=0/12.9

x!=0

x∈R


We add all the numbers together, and all the variables

x/12.9x-(9.9x+34)+10=0

We get rid of parentheses

x/12.9x-9.9x-34+10=0

We multiply all the terms by the denominator


x-(9.9x)*12.9x-34*12.9x+10*12.9x=0

We add all the numbers together, and all the variables

x-(+9.9x)*12.9x-34*12.9x+10*12.9x=0

We multiply parentheses

-108x^2+x-34*12.9x+10*12.9x=0

Wy multiply elements

-108x^2+x-408x+120x=0

We add all the numbers together, and all the variables

-108x^2-287x=0

a = -108; b = -287; c = 0;
Δ = b2-4ac
Δ = -2872-4·(-108)·0
Δ = 82369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82369}=287$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-287)-287}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-287)+287}{2*-108}=\frac{574}{-216}
=-2+71/108
$