2x+2=4/9x

Solution for 2x+2=4/9x equation:

2x+2=4/9x

We move all terms to the left:

2x+2-(4/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4/9x)+2=0

We get rid of parentheses

2x-4/9x+2=0

We multiply all the terms by the denominator


2x*9x+2*9x-4=0

Wy multiply elements

18x^2+18x-4=0

a = 18; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·18·(-4)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{17}}{2*18}=\frac{-18-6\sqrt{17}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{17}}{2*18}=\frac{-18+6\sqrt{17}}{36}
$