45=(3w-6)(w)

Solution for 45=(3w-6)(w) equation:

45=(3w-6)(w)

We move all terms to the left:

45-((3w-6)(w))=0


We calculate terms in parentheses: -((3w-6)w), so:

(3w-6)w

We multiply parentheses

3w^2-6w

Back to the equation:

-(3w^2-6w)


We get rid of parentheses

-3w^2+6w+45=0

a = -3; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-3)·45
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*-3}=\frac{-30}{-6}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*-3}=\frac{18}{-6}
=-3
$