16n^2+100n-100=0

Solution for 16n^2+100n-100=0 equation:

16n^2+100n-100=0

a = 16; b = 100; c = -100;
Δ = b2-4ac
Δ = 1002-4·16·(-100)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{41}}{2*16}=\frac{-100-20\sqrt{41}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{41}}{2*16}=\frac{-100+20\sqrt{41}}{32}
$