27x^2+108x-81=0

Solution for 27x^2+108x-81=0 equation:

27x^2+108x-81=0

a = 27; b = 108; c = -81;
Δ = b2-4ac
Δ = 1082-4·27·(-81)
Δ = 20412
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:

$\sqrt{\Delta}=\sqrt{20412}=\sqrt{2916*7}=\sqrt{2916}*\sqrt{7}=54\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-54\sqrt{7}}{2*27}=\frac{-108-54\sqrt{7}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+54\sqrt{7}}{2*27}=\frac{-108+54\sqrt{7}}{54}
$