4w+8=6w(1w-1)-2w

Solution for 4w+8=6w(1w-1)-2w equation:

4w+8=6w(1w-1)-2w

We move all terms to the left:

4w+8-(6w(1w-1)-2w)=0

We add all the numbers together, and all the variables

4w-(6w(w-1)-2w)+8=0


We calculate terms in parentheses: -(6w(w-1)-2w), so:

6w(w-1)-2w

We add all the numbers together, and all the variables

-2w+6w(w-1)

We multiply parentheses

6w^2-2w-6w

We add all the numbers together, and all the variables

6w^2-8w

Back to the equation:

-(6w^2-8w)


We get rid of parentheses

-6w^2+4w+8w+8=0

We add all the numbers together, and all the variables

-6w^2+12w+8=0

a = -6; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·(-6)·8
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*-6}=\frac{-12-4\sqrt{21}}{-12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*-6}=\frac{-12+4\sqrt{21}}{-12}
$