8n^2+6n=5

Solution for 8n^2+6n=5 equation:

8n^2+6n=5

We move all terms to the left:

8n^2+6n-(5)=0

a = 8; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·8·(-5)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*8}=\frac{-20}{16}
=-1+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*8}=\frac{8}{16}
=1/2
$