0=9x^2+54x+55

Solution for 0=9x^2+54x+55 equation:

0=9x^2+54x+55

We move all terms to the left:

0-(9x^2+54x+55)=0

We add all the numbers together, and all the variables

-(9x^2+54x+55)=0

We get rid of parentheses

-9x^2-54x-55=0

a = -9; b = -54; c = -55;
Δ = b2-4ac
Δ = -542-4·(-9)·(-55)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{26}}{2*-9}=\frac{54-6\sqrt{26}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{26}}{2*-9}=\frac{54+6\sqrt{26}}{-18}
$