27x^2-165x-180=0

Solution for 27x^2-165x-180=0 equation:

27x^2-165x-180=0

a = 27; b = -165; c = -180;
Δ = b2-4ac
Δ = -1652-4·27·(-180)
Δ = 46665
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:

$\sqrt{\Delta}=\sqrt{46665}=\sqrt{9*5185}=\sqrt{9}*\sqrt{5185}=3\sqrt{5185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-3\sqrt{5185}}{2*27}=\frac{165-3\sqrt{5185}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+3\sqrt{5185}}{2*27}=\frac{165+3\sqrt{5185}}{54}
$