4n(9+n)=159

Solution for 4n(9+n)=159 equation:

4n(9+n)=159

We move all terms to the left:

4n(9+n)-(159)=0

We add all the numbers together, and all the variables

4n(n+9)-159=0

We multiply parentheses

4n^2+36n-159=0

a = 4; b = 36; c = -159;
Δ = b2-4ac
Δ = 362-4·4·(-159)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-16\sqrt{15}}{2*4}=\frac{-36-16\sqrt{15}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+16\sqrt{15}}{2*4}=\frac{-36+16\sqrt{15}}{8}
$