0=9x2-9x-4

Solution for 0=9x2-9x-4 equation:

0=9x^2-9x-4

We move all terms to the left:

0-(9x^2-9x-4)=0

We add all the numbers together, and all the variables

-(9x^2-9x-4)=0

We get rid of parentheses

-9x^2+9x+4=0

a = -9; b = 9; c = +4;
Δ = b2-4ac
Δ = 92-4·(-9)·4
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*-9}=\frac{-24}{-18}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*-9}=\frac{6}{-18}
=-1/3
$