11v^2=-12v+3

Solution for 11v^2=-12v+3 equation:

11v^2=-12v+3

We move all terms to the left:

11v^2-(-12v+3)=0

We get rid of parentheses

11v^2+12v-3=0

a = 11; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·11·(-3)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{69}}{2*11}=\frac{-12-2\sqrt{69}}{22}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{69}}{2*11}=\frac{-12+2\sqrt{69}}{22}
$