4w+2/3w-9=2

Solution for 4w+2/3w-9=2 equation:

4w+2/3w-9=2

We move all terms to the left:

4w+2/3w-9-(2)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

4w+2/3w-11=0

We multiply all the terms by the denominator


4w*3w-11*3w+2=0

Wy multiply elements

12w^2-33w+2=0

a = 12; b = -33; c = +2;
Δ = b2-4ac
Δ = -332-4·12·2
Δ = 993
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{-(-33)-\sqrt{993}}{2*12}=\frac{33-\sqrt{993}}{24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{993}}{2*12}=\frac{33+\sqrt{993}}{24}
$