6n^2-89n-1127=0

Solution for 6n^2-89n-1127=0 equation:

6n^2-89n-1127=0

a = 6; b = -89; c = -1127;
Δ = b2-4ac
Δ = -892-4·6·(-1127)
Δ = 34969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34969}=187$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-187}{2*6}=\frac{-98}{12}
=-8+1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+187}{2*6}=\frac{276}{12}
=23
$