4n^2+16n-34=-2

Solution for 4n^2+16n-34=-2 equation:

4n^2+16n-34=-2

We move all terms to the left:

4n^2+16n-34-(-2)=0

We add all the numbers together, and all the variables

4n^2+16n-32=0

a = 4; b = 16; c = -32;
Δ = b2-4ac
Δ = 162-4·4·(-32)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{3}}{2*4}=\frac{-16-16\sqrt{3}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{3}}{2*4}=\frac{-16+16\sqrt{3}}{8}
$