8n^2+2n-1138=0

Solution for 8n^2+2n-1138=0 equation:

8n^2+2n-1138=0

a = 8; b = 2; c = -1138;
Δ = b2-4ac
Δ = 22-4·8·(-1138)
Δ = 36420
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:

$\sqrt{\Delta}=\sqrt{36420}=\sqrt{4*9105}=\sqrt{4}*\sqrt{9105}=2\sqrt{9105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{9105}}{2*8}=\frac{-2-2\sqrt{9105}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{9105}}{2*8}=\frac{-2+2\sqrt{9105}}{16}
$