a(2/9)=1/9

Solution for a(2/9)=1/9 equation:

a(2/9)=1/9

We move all terms to the left:

a(2/9)-(1/9)=0

We add all the numbers together, and all the variables

a(+2/9)-(+1/9)=0

We multiply parentheses

2a^2-(+1/9)=0

We get rid of parentheses

2a^2-1/9=0

We multiply all the terms by the denominator


2a^2*9-1=0

Wy multiply elements

18a^2-1=0

a = 18; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·18·(-1)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*18}=\frac{0-6\sqrt{2}}{36}
=-\frac{6\sqrt{2}}{36}
=-\frac{\sqrt{2}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*18}=\frac{0+6\sqrt{2}}{36}
=\frac{6\sqrt{2}}{36}
=\frac{\sqrt{2}}{6}
$