9x(5/9)=1

Solution for 9x(5/9)=1 equation:

9x(5/9)=1

We move all terms to the left:

9x(5/9)-(1)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

45x^2-1=0

a = 45; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·45·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*45}=\frac{0-6\sqrt{5}}{90}
=-\frac{6\sqrt{5}}{90}
=-\frac{\sqrt{5}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*45}=\frac{0+6\sqrt{5}}{90}
=\frac{6\sqrt{5}}{90}
=\frac{\sqrt{5}}{15}
$