8n^2-6n-4=0

Solution for 8n^2-6n-4=0 equation:

8n^2-6n-4=0

a = 8; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·8·(-4)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{41}}{2*8}=\frac{6-2\sqrt{41}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{41}}{2*8}=\frac{6+2\sqrt{41}}{16}
$