-24=5w(w-4)-7w

Solution for -24=5w(w-4)-7w equation:

-24=5w(w-4)-7w

We move all terms to the left:

-24-(5w(w-4)-7w)=0


We calculate terms in parentheses: -(5w(w-4)-7w), so:

5w(w-4)-7w

We add all the numbers together, and all the variables

-7w+5w(w-4)

We multiply parentheses

5w^2-7w-20w

We add all the numbers together, and all the variables

5w^2-27w

Back to the equation:

-(5w^2-27w)


We get rid of parentheses

-5w^2+27w-24=0

a = -5; b = 27; c = -24;
Δ = b2-4ac
Δ = 272-4·(-5)·(-24)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{249}}{2*-5}=\frac{-27-\sqrt{249}}{-10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{249}}{2*-5}=\frac{-27+\sqrt{249}}{-10}
$