3/9x+(5/9x+86)=x

Solution for 3/9x+(5/9x+86)=x equation:

3/9x+(5/9x+86)=x

We move all terms to the left:

3/9x+(5/9x+86)-(x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 9x+86)!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/9x+(5/9x+86)=0

We get rid of parentheses

-1x+3/9x+5/9x+86=0

We multiply all the terms by the denominator


-1x*9x+86*9x+3+5=0

We add all the numbers together, and all the variables

-1x*9x+86*9x+8=0

Wy multiply elements

-9x^2+774x+8=0

a = -9; b = 774; c = +8;
Δ = b2-4ac
Δ = 7742-4·(-9)·8
Δ = 599364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{599364}=\sqrt{36*16649}=\sqrt{36}*\sqrt{16649}=6\sqrt{16649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(774)-6\sqrt{16649}}{2*-9}=\frac{-774-6\sqrt{16649}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(774)+6\sqrt{16649}}{2*-9}=\frac{-774+6\sqrt{16649}}{-18}
$