50=v+0.05v^2

Solution for 50=v+0.05v^2 equation:

50=v+0.05v^2

We move all terms to the left:

50-(v+0.05v^2)=0

We get rid of parentheses

-0.05v^2-v+50=0

We add all the numbers together, and all the variables

-0.05v^2-1v+50=0

a = -0.05; b = -1; c = +50;
Δ = b2-4ac
Δ = -12-4·(-0.05)·50
Δ = 11
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{11}}{2*-0.05}=\frac{1-\sqrt{11}}{-0.1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{11}}{2*-0.05}=\frac{1+\sqrt{11}}{-0.1}
$