24=(6+3w)w

Solution for 24=(6+3w)w equation:

24=(6+3w)w

We move all terms to the left:

24-((6+3w)w)=0

We add all the numbers together, and all the variables

-((3w+6)w)+24=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+24=0

a = -3; b = -6; c = +24;
Δ = b2-4ac
Δ = -62-4·(-3)·24
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-3}=\frac{-12}{-6}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-3}=\frac{24}{-6}
=-4
$