(W-6)^2=2w^2-11w+6

Solution for (W-6)^2=2w^2-11w+6 equation:

(-6)^2=2W^2-11W+6

We move all terms to the left:

(-6)^2-(2W^2-11W+6)=0

We add all the numbers together, and all the variables

-(2W^2-11W+6)+36=0

We get rid of parentheses

-2W^2+11W-6+36=0

We add all the numbers together, and all the variables

-2W^2+11W+30=0

a = -2; b = 11; c = +30;
Δ = b2-4ac
Δ = 112-4·(-2)·30
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*-2}=\frac{-30}{-4}
=7+1/2
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*-2}=\frac{8}{-4}
=-2
$