5(n^2-5)=-20n

Solution for 5(n^2-5)=-20n equation:

5(n^2-5)=-20n

We move all terms to the left:

5(n^2-5)-(-20n)=0

We multiply parentheses

5n^2-(-20n)-25=0

We get rid of parentheses

5n^2+20n-25=0

a = 5; b = 20; c = -25;
Δ = b2-4ac
Δ = 202-4·5·(-25)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-30}{2*5}=\frac{-50}{10}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+30}{2*5}=\frac{10}{10}
=1
$