-4n(2n+7)=20

Solution for -4n(2n+7)=20 equation:

-4n(2n+7)=20

We move all terms to the left:

-4n(2n+7)-(20)=0

We multiply parentheses

-8n^2-28n-20=0

a = -8; b = -28; c = -20;
Δ = b2-4ac
Δ = -282-4·(-8)·(-20)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12}{2*-8}=\frac{16}{-16}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12}{2*-8}=\frac{40}{-16}
=-2+1/2
$