(w-6)(w-6)=2w^2-10w+12

Solution for (w-6)(w-6)=2w^2-10w+12 equation:

(w-6)(w-6)=2w^2-10w+12

We move all terms to the left:

(w-6)(w-6)-(2w^2-10w+12)=0

We get rid of parentheses

-2w^2+(w-6)(w-6)+10w-12=0

We multiply parentheses ..

-2w^2+(+w^2-6w-6w+36)+10w-12=0

We get rid of parentheses

-2w^2+w^2-6w-6w+10w+36-12=0

We add all the numbers together, and all the variables

-1w^2-2w+24=0

a = -1; b = -2; c = +24;
Δ = b2-4ac
Δ = -22-4·(-1)·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-1}=\frac{-8}{-2}
=+4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-1}=\frac{12}{-2}
=-6
$