2n(2n-14)=-24

Solution for 2n(2n-14)=-24 equation:

2n(2n-14)=-24

We move all terms to the left:

2n(2n-14)-(-24)=0

We add all the numbers together, and all the variables

2n(2n-14)+24=0

We multiply parentheses

4n^2-28n+24=0

a = 4; b = -28; c = +24;
Δ = b2-4ac
Δ = -282-4·4·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20}{2*4}=\frac{8}{8}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20}{2*4}=\frac{48}{8}
=6
$