5r^2-3r+1=3r^2

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

5r^2-3r+1=3r^2

We move all terms to the left:

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

determiningTheFunctionDomain
5r^2-3r^2-3r+1=0

We add all the numbers together, and all the variables

2r^2-3r+1=0

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

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