0=9x^2+30x+17

Solution for 0=9x^2+30x+17 equation:

0=9x^2+30x+17

We move all terms to the left:

0-(9x^2+30x+17)=0

We add all the numbers together, and all the variables

-(9x^2+30x+17)=0

We get rid of parentheses

-9x^2-30x-17=0

a = -9; b = -30; c = -17;
Δ = b2-4ac
Δ = -302-4·(-9)·(-17)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12\sqrt{2}}{2*-9}=\frac{30-12\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{2}}{2*-9}=\frac{30+12\sqrt{2}}{-18}
$