10n(5-n)-1=29

Solution for 10n(5-n)-1=29 equation:

10n(5-n)-1=29

We move all terms to the left:

10n(5-n)-1-(29)=0

We add all the numbers together, and all the variables

10n(-1n+5)-1-29=0

We add all the numbers together, and all the variables

10n(-1n+5)-30=0

We multiply parentheses

-10n^2+50n-30=0

a = -10; b = 50; c = -30;
Δ = b2-4ac
Δ = 502-4·(-10)·(-30)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{13}}{2*-10}=\frac{-50-10\sqrt{13}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{13}}{2*-10}=\frac{-50+10\sqrt{13}}{-20}
$