8n^2=31n-21

Solution for 8n^2=31n-21 equation:

8n^2=31n-21

We move all terms to the left:

8n^2-(31n-21)=0

We get rid of parentheses

8n^2-31n+21=0

a = 8; b = -31; c = +21;
Δ = b2-4ac
Δ = -312-4·8·21
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-17}{2*8}=\frac{14}{16}
=7/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+17}{2*8}=\frac{48}{16}
=3
$