-24=-6w+4w(w-5)

Solution for -24=-6w+4w(w-5) equation:

-24=-6w+4w(w-5)

We move all terms to the left:

-24-(-6w+4w(w-5))=0


We calculate terms in parentheses: -(-6w+4w(w-5)), so:

-6w+4w(w-5)

We multiply parentheses

4w^2-6w-20w

We add all the numbers together, and all the variables

4w^2-26w

Back to the equation:

-(4w^2-26w)


We get rid of parentheses

-4w^2+26w-24=0

a = -4; b = 26; c = -24;
Δ = b2-4ac
Δ = 262-4·(-4)·(-24)
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{73}}{2*-4}=\frac{-26-2\sqrt{73}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{73}}{2*-4}=\frac{-26+2\sqrt{73}}{-8}
$