54x^2+27x-27=0

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

54x^2+27x-27=0

a = 54; b = 27; c = -27;
Δ = b2-4ac
Δ = 272-4·54·(-27)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-81}{2*54}=\frac{-108}{108}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+81}{2*54}=\frac{54}{108}
=1/2
$