8n^2-67n+24=0

Solution for 8n^2-67n+24=0 equation:

8n^2-67n+24=0

a = 8; b = -67; c = +24;
Δ = b2-4ac
Δ = -672-4·8·24
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-61}{2*8}=\frac{6}{16}
=3/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+61}{2*8}=\frac{128}{16}
=8
$