3w^2+6w-4=9-2w

Solution for 3w^2+6w-4=9-2w equation:

3w^2+6w-4=9-2w

We move all terms to the left:

3w^2+6w-4-(9-2w)=0

We add all the numbers together, and all the variables

3w^2+6w-(-2w+9)-4=0

We get rid of parentheses

3w^2+6w+2w-9-4=0

We add all the numbers together, and all the variables

3w^2+8w-13=0

a = 3; b = 8; c = -13;
Δ = b2-4ac
Δ = 82-4·3·(-13)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{55}}{2*3}=\frac{-8-2\sqrt{55}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{55}}{2*3}=\frac{-8+2\sqrt{55}}{6}
$