w^2-6w+9=2w^2-2w-3

Solution for w^2-6w+9=2w^2-2w-3 equation:

w^2-6w+9=2w^2-2w-3

We move all terms to the left:

w^2-6w+9-(2w^2-2w-3)=0

We get rid of parentheses

w^2-2w^2-6w+2w+3+9=0

We add all the numbers together, and all the variables

-1w^2-4w+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$