5n^2-2n-306=0

Solution for 5n^2-2n-306=0 equation:

5n^2-2n-306=0

a = 5; b = -2; c = -306;
Δ = b2-4ac
Δ = -22-4·5·(-306)
Δ = 6124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6124}=\sqrt{4*1531}=\sqrt{4}*\sqrt{1531}=2\sqrt{1531}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{1531}}{2*5}=\frac{2-2\sqrt{1531}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{1531}}{2*5}=\frac{2+2\sqrt{1531}}{10}
$