8n^2+31n+4=8

Solution for 8n^2+31n+4=8 equation:

8n^2+31n+4=8

We move all terms to the left:

8n^2+31n+4-(8)=0

We add all the numbers together, and all the variables

8n^2+31n-4=0

a = 8; b = 31; c = -4;
Δ = b2-4ac
Δ = 312-4·8·(-4)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-33}{2*8}=\frac{-64}{16}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+33}{2*8}=\frac{2}{16}
=1/8
$