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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8w^2-2w-40w-(-4(w-2))=0


We calculate terms in parentheses: -(-4(w-2)), so:

-4(w-2)

We multiply parentheses

-4w+8

Back to the equation:

-(-4w+8)


We add all the numbers together, and all the variables

8w^2-42w-(-4w+8)=0

We get rid of parentheses

8w^2-42w+4w-8=0

We add all the numbers together, and all the variables

8w^2-38w-8=0

a = 8; b = -38; c = -8;
Δ = b2-4ac
Δ = -382-4·8·(-8)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-10\sqrt{17}}{2*8}=\frac{38-10\sqrt{17}}{16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+10\sqrt{17}}{2*8}=\frac{38+10\sqrt{17}}{16}
$