180=w(2w-9)

Solution for 180=w(2w-9) equation:

180=w(2w-9)

We move all terms to the left:

180-(w(2w-9))=0


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

w(2w-9)

We multiply parentheses

2w^2-9w

Back to the equation:

-(2w^2-9w)


We get rid of parentheses

-2w^2+9w+180=0

a = -2; b = 9; c = +180;
Δ = b2-4ac
Δ = 92-4·(-2)·180
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*-2}=\frac{-48}{-4}
=+12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*-2}=\frac{30}{-4}
=-7+1/2
$