n2+4n-92=0

Solution for n2+4n-92=0 equation:

n2+4n-92=0

We add all the numbers together, and all the variables

n^2+4n-92=0

a = 1; b = 4; c = -92;
Δ = b2-4ac
Δ = 42-4·1·(-92)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{6}}{2*1}=\frac{-4-8\sqrt{6}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{6}}{2*1}=\frac{-4+8\sqrt{6}}{2}
$