21v=8v*8v-9

Solution for 21v=8v*8v-9 equation:

21v=8v*8v-9

We move all terms to the left:

21v-(8v*8v-9)=0

We get rid of parentheses

21v-8v*8v+9=0

Wy multiply elements

-64v^2+21v+9=0

a = -64; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·(-64)·9
Δ = 2745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2745}=\sqrt{9*305}=\sqrt{9}*\sqrt{305}=3\sqrt{305}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{305}}{2*-64}=\frac{-21-3\sqrt{305}}{-128}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{305}}{2*-64}=\frac{-21+3\sqrt{305}}{-128}
$