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

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

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

We move all terms to the left:

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


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

6(w-1)2w

We multiply parentheses

12w^2-12w

Back to the equation:

-(12w^2-12w)


We get rid of parentheses

-12w^2+4w+12w+8=0

We add all the numbers together, and all the variables

-12w^2+16w+8=0

a = -12; b = 16; c = +8;
Δ = b2-4ac
Δ = 162-4·(-12)·8
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{10}}{2*-12}=\frac{-16-8\sqrt{10}}{-24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{10}}{2*-12}=\frac{-16+8\sqrt{10}}{-24}
$