(2/9)x+5/9=3

Solution for (2/9)x+5/9=3 equation:

(2/9)x+5/9=3

We move all terms to the left:

(2/9)x+5/9-(3)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(2/9)x-3+5/9=0

We add all the numbers together, and all the variables

(+2/9)x-3+5/9=0

We multiply parentheses

2x^2-3+5/9=0

We multiply all the terms by the denominator


2x^2*9+5-3*9=0

We add all the numbers together, and all the variables

2x^2*9-22=0

Wy multiply elements

18x^2-22=0

a = 18; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·18·(-22)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*18}=\frac{0-12\sqrt{11}}{36}
=-\frac{12\sqrt{11}}{36}
=-\frac{\sqrt{11}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*18}=\frac{0+12\sqrt{11}}{36}
=\frac{12\sqrt{11}}{36}
=\frac{\sqrt{11}}{3}
$