5w+8(-w)=6w(-2)(w-4)

Solution for 5w+8(-w)=6w(-2)(w-4) equation:

5w+8(-w)=6w(-2)(w-4)

We move all terms to the left:

5w+8(-w)-(6w(-2)(w-4))=0

We add all the numbers together, and all the variables

5w+8(-1w)-(6w(-2)(w-4))=0

We multiply parentheses

5w-8w-(6w(-2)(w-4))=0

We multiply parentheses ..

5w-8w-(6w(-2w+8))=0


We calculate terms in parentheses: -(6w(-2w+8)), so:

6w(-2w+8)

We multiply parentheses

-12w^2+48w

Back to the equation:

-(-12w^2+48w)


We add all the numbers together, and all the variables

-(-12w^2+48w)-3w=0

We get rid of parentheses

12w^2-48w-3w=0

We add all the numbers together, and all the variables

12w^2-51w=0

a = 12; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·12·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*12}=\frac{0}{24}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*12}=\frac{102}{24}
=4+1/4
$