0=9x^2+17x+6

Solution for 0=9x^2+17x+6 equation:

0=9x^2+17x+6

We move all terms to the left:

0-(9x^2+17x+6)=0

We add all the numbers together, and all the variables

-(9x^2+17x+6)=0

We get rid of parentheses

-9x^2-17x-6=0

a = -9; b = -17; c = -6;
Δ = b2-4ac
Δ = -172-4·(-9)·(-6)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{73}}{2*-9}=\frac{17-\sqrt{73}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{73}}{2*-9}=\frac{17+\sqrt{73}}{-18}
$