9(-2n-8)n=4

Solution for 9(-2n-8)n=4 equation:

9(-2n-8)n=4

We move all terms to the left:

9(-2n-8)n-(4)=0

We multiply parentheses

-18n^2-72n-4=0

a = -18; b = -72; c = -4;
Δ = b2-4ac
Δ = -722-4·(-18)·(-4)
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{34}}{2*-18}=\frac{72-12\sqrt{34}}{-36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{34}}{2*-18}=\frac{72+12\sqrt{34}}{-36}
$