5v^2=11+2v

Solution for 5v^2=11+2v equation:

5v^2=11+2v

We move all terms to the left:

5v^2-(11+2v)=0

We add all the numbers together, and all the variables

5v^2-(2v+11)=0

We get rid of parentheses

5v^2-2v-11=0

a = 5; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·5·(-11)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{14}}{2*5}=\frac{2-4\sqrt{14}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{14}}{2*5}=\frac{2+4\sqrt{14}}{10}
$