27x^2-18x-585=0

Solution for 27x^2-18x-585=0 equation:

27x^2-18x-585=0

a = 27; b = -18; c = -585;
Δ = b2-4ac
Δ = -182-4·27·(-585)
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-252}{2*27}=\frac{-234}{54}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+252}{2*27}=\frac{270}{54}
=5
$