W^2+6+9=2w^2+11w+15

Solution for W^2+6+9=2w^2+11w+15 equation:

^2+6+9=2W^2+11W+15

We move all terms to the left:

^2+6+9-(2W^2+11W+15)=0

We add all the numbers together, and all the variables

-(2W^2+11W+15)=0

We get rid of parentheses

-2W^2-11W-15=0

a = -2; b = -11; c = -15;
Δ = b2-4ac
Δ = -112-4·(-2)·(-15)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*-2}=\frac{10}{-4}
=-2+1/2
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*-2}=\frac{12}{-4}
=-3
$