2w-4=3(w+6)2w-4=3w+18-2w-2w

Solution for 2w-4=3(w+6)2w-4=3w+18-2w-2w equation:

2w-4=3(w+6)2w-4=3w+18-2w-2w

We move all terms to the left:

2w-4-(3(w+6)2w-4)=0


We calculate terms in parentheses: -(3(w+6)2w-4), so:

3(w+6)2w-4

We multiply parentheses

6w^2+36w-4

Back to the equation:

-(6w^2+36w-4)


We get rid of parentheses

-6w^2+2w-36w+4-4=0

We add all the numbers together, and all the variables

-6w^2-34w=0

a = -6; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·(-6)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*-6}=\frac{0}{-12}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*-6}=\frac{68}{-12}
=-5+2/3
$