14v^2=11v-2

Solution for 14v^2=11v-2 equation:

14v^2=11v-2

We move all terms to the left:

14v^2-(11v-2)=0

We get rid of parentheses

14v^2-11v+2=0

a = 14; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·14·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*14}=\frac{8}{28}
=2/7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*14}=\frac{14}{28}
=1/2
$