n^2-15n-9=0

Solution for n^2-15n-9=0 equation:

n^2-15n-9=0

a = 1; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·1·(-9)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{29}}{2*1}=\frac{15-3\sqrt{29}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{29}}{2*1}=\frac{15+3\sqrt{29}}{2}
$