0=17x^2-36x+9

Solution for 0=17x^2-36x+9 equation:

0=17x^2-36x+9

We move all terms to the left:

0-(17x^2-36x+9)=0

We add all the numbers together, and all the variables

-(17x^2-36x+9)=0

We get rid of parentheses

-17x^2+36x-9=0

a = -17; b = 36; c = -9;
Δ = b2-4ac
Δ = 362-4·(-17)·(-9)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{19}}{2*-17}=\frac{-36-6\sqrt{19}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{19}}{2*-17}=\frac{-36+6\sqrt{19}}{-34}
$