W^2+6w+9=2w^2+8w-6

Solution for W^2+6w+9=2w^2+8w-6 equation:

^2+6W+9=2W^2+8W-6

We move all terms to the left:

^2+6W+9-(2W^2+8W-6)=0

We add all the numbers together, and all the variables

6W-(2W^2+8W-6)=0

We get rid of parentheses

-2W^2+6W-8W+6=0

We add all the numbers together, and all the variables

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

a = -2; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-2)·6
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-2}=\frac{2-2\sqrt{13}}{-4}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-2}=\frac{2+2\sqrt{13}}{-4}
$