9=(2w-3)w

Solution for 9=(2w-3)w equation:

9=(2w-3)w

We move all terms to the left:

9-((2w-3)w)=0


We calculate terms in parentheses: -((2w-3)w), so:

(2w-3)w

We multiply parentheses

2w^2-3w

Back to the equation:

-(2w^2-3w)


We get rid of parentheses

-2w^2+3w+9=0

a = -2; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-2)·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-2}=\frac{-12}{-4}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-2}=\frac{6}{-4}
=-1+1/2
$