2/3w+12=3w-6

Solution for 2/3w+12=3w-6 equation:

2/3w+12=3w-6

We move all terms to the left:

2/3w+12-(3w-6)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We get rid of parentheses

2/3w-3w+6+12=0

We multiply all the terms by the denominator


-3w*3w+6*3w+12*3w+2=0

Wy multiply elements

-9w^2+18w+36w+2=0

We add all the numbers together, and all the variables

-9w^2+54w+2=0

a = -9; b = 54; c = +2;
Δ = b2-4ac
Δ = 542-4·(-9)·2
Δ = 2988
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:

$\sqrt{\Delta}=\sqrt{2988}=\sqrt{36*83}=\sqrt{36}*\sqrt{83}=6\sqrt{83}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{83}}{2*-9}=\frac{-54-6\sqrt{83}}{-18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{83}}{2*-9}=\frac{-54+6\sqrt{83}}{-18}
$