7v^2-37v+72=3v^2-v

Solution for 7v^2-37v+72=3v^2-v equation:

7v^2-37v+72=3v^2-v

We move all terms to the left:

7v^2-37v+72-(3v^2-v)=0

We get rid of parentheses

7v^2-3v^2-37v+v+72=0

We add all the numbers together, and all the variables

4v^2-36v+72=0

a = 4; b = -36; c = +72;
Δ = b2-4ac
Δ = -362-4·4·72
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12}{2*4}=\frac{24}{8}
=3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12}{2*4}=\frac{48}{8}
=6
$