n2+9n-188=0

Solution for n2+9n-188=0 equation:

n2+9n-188=0

We add all the numbers together, and all the variables

n^2+9n-188=0

a = 1; b = 9; c = -188;
Δ = b2-4ac
Δ = 92-4·1·(-188)
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7\sqrt{17}}{2*1}=\frac{-9-7\sqrt{17}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7\sqrt{17}}{2*1}=\frac{-9+7\sqrt{17}}{2}
$