-3(w+5)w=2(w-6)

Solution for -3(w+5)w=2(w-6) equation:

-3(w+5)w=2(w-6)

We move all terms to the left:

-3(w+5)w-(2(w-6))=0

We multiply parentheses

-3w^2-15w-(2(w-6))=0


We calculate terms in parentheses: -(2(w-6)), so:

2(w-6)

We multiply parentheses

2w-12

Back to the equation:

-(2w-12)


We get rid of parentheses

-3w^2-15w-2w+12=0

We add all the numbers together, and all the variables

-3w^2-17w+12=0

a = -3; b = -17; c = +12;
Δ = b2-4ac
Δ = -172-4·(-3)·12
Δ = 433
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{-(-17)-\sqrt{433}}{2*-3}=\frac{17-\sqrt{433}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{433}}{2*-3}=\frac{17+\sqrt{433}}{-6}
$