5(n-4)n=10

Solution for 5(n-4)n=10 equation:

5(n-4)n=10

We move all terms to the left:

5(n-4)n-(10)=0

We multiply parentheses

5n^2-20n-10=0

a = 5; b = -20; c = -10;
Δ = b2-4ac
Δ = -202-4·5·(-10)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{6}}{2*5}=\frac{20-10\sqrt{6}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{6}}{2*5}=\frac{20+10\sqrt{6}}{10}
$