3w(2w-3)=-2(w+1)

Solution for 3w(2w-3)=-2(w+1) equation:

3w(2w-3)=-2(w+1)

We move all terms to the left:

3w(2w-3)-(-2(w+1))=0

We multiply parentheses

6w^2-9w-(-2(w+1))=0


We calculate terms in parentheses: -(-2(w+1)), so:

-2(w+1)

We multiply parentheses

-2w-2

Back to the equation:

-(-2w-2)


We get rid of parentheses

6w^2-9w+2w+2=0

We add all the numbers together, and all the variables

6w^2-7w+2=0

a = 6; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*6}=\frac{6}{12}
=1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*6}=\frac{8}{12}
=2/3
$