0=9x^2-27x+8

Solution for 0=9x^2-27x+8 equation:

0=9x^2-27x+8

We move all terms to the left:

0-(9x^2-27x+8)=0

We add all the numbers together, and all the variables

-(9x^2-27x+8)=0

We get rid of parentheses

-9x^2+27x-8=0

a = -9; b = 27; c = -8;
Δ = b2-4ac
Δ = 272-4·(-9)·(-8)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-21}{2*-9}=\frac{-48}{-18}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+21}{2*-9}=\frac{-6}{-18}
=1/3
$