9x2-6x+5/9=0

Solution for 9x2-6x+5/9=0 equation:

9x^2-6x+5/9=0

We multiply all the terms by the denominator


9x^2*9-6x*9+5=0

Wy multiply elements

81x^2-54x+5=0

a = 81; b = -54; c = +5;
Δ = b2-4ac
Δ = -542-4·81·5
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-36}{2*81}=\frac{18}{162}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+36}{2*81}=\frac{90}{162}
=5/9
$