0=9x^2-6x-5

Solution for 0=9x^2-6x-5 equation:

0=9x^2-6x-5

We move all terms to the left:

0-(9x^2-6x-5)=0

We add all the numbers together, and all the variables

-(9x^2-6x-5)=0

We get rid of parentheses

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

a = -9; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-9)·5
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*-9}=\frac{-6-6\sqrt{6}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*-9}=\frac{-6+6\sqrt{6}}{-18}
$