5v^2-3v+1=3

Solution for 5v^2-3v+1=3 equation:

5v^2-3v+1=3

We move all terms to the left:

5v^2-3v+1-(3)=0

We add all the numbers together, and all the variables

5v^2-3v-2=0

a = 5; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*5}=\frac{-4}{10}
=-2/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*5}=\frac{10}{10}
=1
$