-6(w+1)8w=2(w-3)

Solution for -6(w+1)8w=2(w-3) equation:

-6(w+1)8w=2(w-3)

We move all terms to the left:

-6(w+1)8w-(2(w-3))=0

We multiply parentheses

-48w^2-48w-(2(w-3))=0


We calculate terms in parentheses: -(2(w-3)), so:

2(w-3)

We multiply parentheses

2w-6

Back to the equation:

-(2w-6)


We get rid of parentheses

-48w^2-48w-2w+6=0

We add all the numbers together, and all the variables

-48w^2-50w+6=0

a = -48; b = -50; c = +6;
Δ = b2-4ac
Δ = -502-4·(-48)·6
Δ = 3652
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:

$\sqrt{\Delta}=\sqrt{3652}=\sqrt{4*913}=\sqrt{4}*\sqrt{913}=2\sqrt{913}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{913}}{2*-48}=\frac{50-2\sqrt{913}}{-96}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{913}}{2*-48}=\frac{50+2\sqrt{913}}{-96}
$