4v^2=45+8v

Solution for 4v^2=45+8v equation:

4v^2=45+8v

We move all terms to the left:

4v^2-(45+8v)=0

We add all the numbers together, and all the variables

4v^2-(8v+45)=0

We get rid of parentheses

4v^2-8v-45=0

a = 4; b = -8; c = -45;
Δ = b2-4ac
Δ = -82-4·4·(-45)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*4}=\frac{-20}{8}
=-2+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*4}=\frac{36}{8}
=4+1/2
$