2v^2=40-11v

Solution for 2v^2=40-11v equation:

2v^2=40-11v

We move all terms to the left:

2v^2-(40-11v)=0

We add all the numbers together, and all the variables

2v^2-(-11v+40)=0

We get rid of parentheses

2v^2+11v-40=0

a = 2; b = 11; c = -40;
Δ = b2-4ac
Δ = 112-4·2·(-40)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*2}=\frac{-32}{4}
=-8
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*2}=\frac{10}{4}
=2+1/2
$