3w+4-w=5w-2w(w-2)

Solution for 3w+4-w=5w-2w(w-2) equation:

3w+4-w=5w-2w(w-2)

We move all terms to the left:

3w+4-w-(5w-2w(w-2))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(5w-2w(w-2)), so:

5w-2w(w-2)

We multiply parentheses

-2w^2+5w+4w

We add all the numbers together, and all the variables

-2w^2+9w

Back to the equation:

-(-2w^2+9w)


We get rid of parentheses

2w^2-9w+2w+4=0

We add all the numbers together, and all the variables

2w^2-7w+4=0

a = 2; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·2·4
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{17}}{2*2}=\frac{7-\sqrt{17}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{17}}{2*2}=\frac{7+\sqrt{17}}{4}
$