3w^2-2w+1=w^2+3w-1

Solution for 3w^2-2w+1=w^2+3w-1 equation:

3w^2-2w+1=w^2+3w-1

We move all terms to the left:

3w^2-2w+1-(w^2+3w-1)=0

We get rid of parentheses

3w^2-w^2-2w-3w+1+1=0

We add all the numbers together, and all the variables

2w^2-5w+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$