6r^2-10r-100=0

Solution for 6r^2-10r-100=0 equation:

6r^2-10r-100=0

a = 6; b = -10; c = -100;
Δ = b2-4ac
Δ = -102-4·6·(-100)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-50}{2*6}=\frac{-40}{12}
=-3+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+50}{2*6}=\frac{60}{12}
=5
$