v(11v+3)=8

Solution for v(11v+3)=8 equation:

v(11v+3)=8

We move all terms to the left:

v(11v+3)-(8)=0

We multiply parentheses

11v^2+3v-8=0

a = 11; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·11·(-8)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*11}=\frac{-22}{22}
=-1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*11}=\frac{16}{22}
=8/11
$