8n^2-n-12=-8

Solution for 8n^2-n-12=-8 equation:

8n^2-n-12=-8

We move all terms to the left:

8n^2-n-12-(-8)=0

We add all the numbers together, and all the variables

8n^2-1n-4=0

a = 8; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·8·(-4)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{129}}{2*8}=\frac{1-\sqrt{129}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{129}}{2*8}=\frac{1+\sqrt{129}}{16}
$