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

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

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

We move all terms to the left:

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

We multiply parentheses

4w^2-16w-(5(w+4)-2)=0


We calculate terms in parentheses: -(5(w+4)-2), so:

5(w+4)-2

We multiply parentheses

5w+20-2

We add all the numbers together, and all the variables

5w+18

Back to the equation:

-(5w+18)


We get rid of parentheses

4w^2-16w-5w-18=0

We add all the numbers together, and all the variables

4w^2-21w-18=0

a = 4; b = -21; c = -18;
Δ = b2-4ac
Δ = -212-4·4·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-27}{2*4}=\frac{-6}{8}
=-3/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*4}=\frac{48}{8}
=6
$