5w+4-w=9w(w-2)

Solution for 5w+4-w=9w(w-2) equation:

5w+4-w=9w(w-2)

We move all terms to the left:

5w+4-w-(9w(w-2))=0

We add all the numbers together, and all the variables

4w-(9w(w-2))+4=0


We calculate terms in parentheses: -(9w(w-2)), so:

9w(w-2)

We multiply parentheses

9w^2-18w

Back to the equation:

-(9w^2-18w)


We get rid of parentheses

-9w^2+4w+18w+4=0

We add all the numbers together, and all the variables

-9w^2+22w+4=0

a = -9; b = 22; c = +4;
Δ = b2-4ac
Δ = 222-4·(-9)·4
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{157}}{2*-9}=\frac{-22-2\sqrt{157}}{-18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{157}}{2*-9}=\frac{-22+2\sqrt{157}}{-18}
$