3r^2-54r+87=0

Solution for 3r^2-54r+87=0 equation:

3r^2-54r+87=0

a = 3; b = -54; c = +87;
Δ = b2-4ac
Δ = -542-4·3·87
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-12\sqrt{13}}{2*3}=\frac{54-12\sqrt{13}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+12\sqrt{13}}{2*3}=\frac{54+12\sqrt{13}}{6}
$