9x^2+54x+6=0

Solution for 9x^2+54x+6=0 equation:

9x^2+54x+6=0

a = 9; b = 54; c = +6;
Δ = b2-4ac
Δ = 542-4·9·6
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30\sqrt{3}}{2*9}=\frac{-54-30\sqrt{3}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30\sqrt{3}}{2*9}=\frac{-54+30\sqrt{3}}{18}
$