3v^2=5v-2

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

3v^2=5v-2

We move all terms to the left:

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

We get rid of parentheses

3v^2-5v+2=0

a = 3; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·3·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*3}=\frac{4}{6}
=2/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*3}=\frac{6}{6}
=1
$