6n^2-5n-50=0

Solution for 6n^2-5n-50=0 equation:

6n^2-5n-50=0

a = 6; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·6·(-50)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-35}{2*6}=\frac{-30}{12}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*6}=\frac{40}{12}
=3+1/3
$