-n^2+15n=50=0

Solution for -n^2+15n=50=0 equation:

-n^2+15n=50=0

We move all terms to the left:

-n^2+15n-(50)=0

We add all the numbers together, and all the variables

-1n^2+15n-50=0

a = -1; b = 15; c = -50;
Δ = b2-4ac
Δ = 152-4·(-1)·(-50)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5}{2*-1}=\frac{-20}{-2}
=+10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*-1}=\frac{-10}{-2}
=+5
$