0=X^2-18x-9

Solution for 0=X^2-18x-9 equation:

0=X^2-18X-9

We move all terms to the left:

0-(X^2-18X-9)=0

We add all the numbers together, and all the variables

-(X^2-18X-9)=0

We get rid of parentheses

-X^2+18X+9=0

We add all the numbers together, and all the variables

-1X^2+18X+9=0

a = -1; b = 18; c = +9;
Δ = b2-4ac
Δ = 182-4·(-1)·9
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{10}}{2*-1}=\frac{-18-6\sqrt{10}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{10}}{2*-1}=\frac{-18+6\sqrt{10}}{-2}
$