5n^2-n-6=0

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

5n^2-n-6=0

We add all the numbers together, and all the variables

5n^2-1n-6=0

a = 5; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·5·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*5}=\frac{-10}{10}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*5}=\frac{12}{10}
=1+1/5
$