-5n(n-5)=n+13

Solution for -5n(n-5)=n+13 equation:

-5n(n-5)=n+13

We move all terms to the left:

-5n(n-5)-(n+13)=0

We multiply parentheses

-5n^2+25n-(n+13)=0

We get rid of parentheses

-5n^2+25n-n-13=0

We add all the numbers together, and all the variables

-5n^2+24n-13=0

a = -5; b = 24; c = -13;
Δ = b2-4ac
Δ = 242-4·(-5)·(-13)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{79}}{2*-5}=\frac{-24-2\sqrt{79}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{79}}{2*-5}=\frac{-24+2\sqrt{79}}{-10}
$