2w2+2w=9

Solution for 2w2+2w=9 equation:

2w^2+2w=9

We move all terms to the left:

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

a = 2; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·2·(-9)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*2}=\frac{-2-2\sqrt{19}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*2}=\frac{-2+2\sqrt{19}}{4}
$