27x2-72x-192=0

Solution for 27x2-72x-192=0 equation:

27x^2-72x-192=0

a = 27; b = -72; c = -192;
Δ = b2-4ac
Δ = -722-4·27·(-192)
Δ = 25920
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:

$\sqrt{\Delta}=\sqrt{25920}=\sqrt{5184*5}=\sqrt{5184}*\sqrt{5}=72\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72\sqrt{5}}{2*27}=\frac{72-72\sqrt{5}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72\sqrt{5}}{2*27}=\frac{72+72\sqrt{5}}{54}
$