27x^2+54x+7=0

Solution for 27x^2+54x+7=0 equation:

27x^2+54x+7=0

a = 27; b = 54; c = +7;
Δ = b2-4ac
Δ = 542-4·27·7
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-12\sqrt{15}}{2*27}=\frac{-54-12\sqrt{15}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+12\sqrt{15}}{2*27}=\frac{-54+12\sqrt{15}}{54}
$