27x^2-3x-9=0

Solution for 27x^2-3x-9=0 equation:

27x^2-3x-9=0

a = 27; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·27·(-9)
Δ = 981
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:

$\sqrt{\Delta}=\sqrt{981}=\sqrt{9*109}=\sqrt{9}*\sqrt{109}=3\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{109}}{2*27}=\frac{3-3\sqrt{109}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{109}}{2*27}=\frac{3+3\sqrt{109}}{54}
$