8n^2-23n=3

Solution for 8n^2-23n=3 equation:

8n^2-23n=3

We move all terms to the left:

8n^2-23n-(3)=0

a = 8; b = -23; c = -3;
Δ = b2-4ac
Δ = -232-4·8·(-3)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-25}{2*8}=\frac{-2}{16}
=-1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*8}=\frac{48}{16}
=3
$