4n^2+16n-83=-9

Solution for 4n^2+16n-83=-9 equation:

4n^2+16n-83=-9

We move all terms to the left:

4n^2+16n-83-(-9)=0

We add all the numbers together, and all the variables

4n^2+16n-74=0

a = 4; b = 16; c = -74;
Δ = b2-4ac
Δ = 162-4·4·(-74)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12\sqrt{10}}{2*4}=\frac{-16-12\sqrt{10}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12\sqrt{10}}{2*4}=\frac{-16+12\sqrt{10}}{8}
$