0=n^2-10n-15

Solution for 0=n^2-10n-15 equation:

0=n^2-10n-15

We move all terms to the left:

0-(n^2-10n-15)=0

We add all the numbers together, and all the variables

-(n^2-10n-15)=0

We get rid of parentheses

-n^2+10n+15=0

We add all the numbers together, and all the variables

-1n^2+10n+15=0

a = -1; b = 10; c = +15;
Δ = b2-4ac
Δ = 102-4·(-1)·15
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*-1}=\frac{-10-4\sqrt{10}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*-1}=\frac{-10+4\sqrt{10}}{-2}
$