3r^2-108r-54=0

Solution for 3r^2-108r-54=0 equation:

3r^2-108r-54=0

a = 3; b = -108; c = -54;
Δ = b2-4ac
Δ = -1082-4·3·(-54)
Δ = 12312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12312}=\sqrt{324*38}=\sqrt{324}*\sqrt{38}=18\sqrt{38}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-18\sqrt{38}}{2*3}=\frac{108-18\sqrt{38}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+18\sqrt{38}}{2*3}=\frac{108+18\sqrt{38}}{6}
$