8n^2+16n-89=0

Solution for 8n^2+16n-89=0 equation:

8n^2+16n-89=0

a = 8; b = 16; c = -89;
Δ = b2-4ac
Δ = 162-4·8·(-89)
Δ = 3104
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:

$\sqrt{\Delta}=\sqrt{3104}=\sqrt{16*194}=\sqrt{16}*\sqrt{194}=4\sqrt{194}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{194}}{2*8}=\frac{-16-4\sqrt{194}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{194}}{2*8}=\frac{-16+4\sqrt{194}}{16}
$