2/9x+2.2222222222222222222222222222222=2.6666666667x-30

Solution for 2/9x+2.2222222222222222222222222222222=2.6666666667x-30 equation:

2/9x+2.2222222222222222222222222222222=2.6666666667x-30

We move all terms to the left:

2/9x+2.2222222222222222222222222222222-(2.6666666667x-30)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2/9x-(2.6666666667x-30)+2.2222222222222=0

We get rid of parentheses

2/9x-2.6666666667x+30+2.2222222222222=0

We multiply all the terms by the denominator


-(2.6666666667x)*9x+30*9x+(2.2222222222222)*9x+2=0

We add all the numbers together, and all the variables

-(+2.6666666667x)*9x+30*9x+(2.2222222222222)*9x+2=0

We multiply parentheses

-18x^2+30*9x+20x+2=0

Wy multiply elements

-18x^2+270x+20x+2=0

We add all the numbers together, and all the variables

-18x^2+290x+2=0

a = -18; b = 290; c = +2;
Δ = b2-4ac
Δ = 2902-4·(-18)·2
Δ = 84244
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:

$\sqrt{\Delta}=\sqrt{84244}=\sqrt{4*21061}=\sqrt{4}*\sqrt{21061}=2\sqrt{21061}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(290)-2\sqrt{21061}}{2*-18}=\frac{-290-2\sqrt{21061}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(290)+2\sqrt{21061}}{2*-18}=\frac{-290+2\sqrt{21061}}{-36}
$