0=-2v^2+7v+22

Solution for 0=-2v^2+7v+22 equation:

0=-2v^2+7v+22

We move all terms to the left:

0-(-2v^2+7v+22)=0

We add all the numbers together, and all the variables

-(-2v^2+7v+22)=0

We get rid of parentheses

2v^2-7v-22=0

a = 2; b = -7; c = -22;
Δ = b2-4ac
Δ = -72-4·2·(-22)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-15}{2*2}=\frac{-8}{4}
=-2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+15}{2*2}=\frac{22}{4}
=5+1/2
$