2/3w+8=3w-6

Solution for 2/3w+8=3w-6 equation:

2/3w+8=3w-6

We move all terms to the left:

2/3w+8-(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+8=0

We multiply all the terms by the denominator


-3w*3w+6*3w+8*3w+2=0

Wy multiply elements

-9w^2+18w+24w+2=0

We add all the numbers together, and all the variables

-9w^2+42w+2=0

a = -9; b = 42; c = +2;
Δ = b2-4ac
Δ = 422-4·(-9)·2
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{51}}{2*-9}=\frac{-42-6\sqrt{51}}{-18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{51}}{2*-9}=\frac{-42+6\sqrt{51}}{-18}
$