3r^2-6r-77=0

Solution for 3r^2-6r-77=0 equation:

3r^2-6r-77=0

a = 3; b = -6; c = -77;
Δ = b2-4ac
Δ = -62-4·3·(-77)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{15}}{2*3}=\frac{6-8\sqrt{15}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{15}}{2*3}=\frac{6+8\sqrt{15}}{6}
$