50(v)=1.1v+0.05v^2

Solution for 50(v)=1.1v+0.05v^2 equation:

50(v)=1.1v+0.05v^2

We move all terms to the left:

50(v)-(1.1v+0.05v^2)=0

We get rid of parentheses

-0.05v^2-1.1v+50v=0

We add all the numbers together, and all the variables

-0.05v^2+48.9v=0

a = -0.05; b = 48.9; c = 0;
Δ = b2-4ac
Δ = 48.92-4·(-0.05)·0
Δ = 2391.21
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{-(48.9)-\sqrt{2391.21}}{2*-0.05}=\frac{-48.9-\sqrt{2391.21}}{-0.1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48.9)+\sqrt{2391.21}}{2*-0.05}=\frac{-48.9+\sqrt{2391.21}}{-0.1}
$