8n(2n-3)=21

Solution for 8n(2n-3)=21 equation:

8n(2n-3)=21

We move all terms to the left:

8n(2n-3)-(21)=0

We multiply parentheses

16n^2-24n-21=0

a = 16; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·16·(-21)
Δ = 1920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{30}}{2*16}=\frac{24-8\sqrt{30}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{30}}{2*16}=\frac{24+8\sqrt{30}}{32}
$