5/6w+21=-1/3*2w-9

Solution for 5/6w+21=-1/3*2w-9 equation:

5/6w+21=-1/3*2w-9

We move all terms to the left:

5/6w+21-(-1/3*2w-9)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R



Domain of the equation: 3*2w-9)!=0

w∈R


We get rid of parentheses

5/6w+1/3*2w+9+21=0

We calculate fractions


60w/72w^2+6w/72w^2+9+21=0

We add all the numbers together, and all the variables

60w/72w^2+6w/72w^2+30=0

We multiply all the terms by the denominator


60w+6w+30*72w^2=0

We add all the numbers together, and all the variables

66w+30*72w^2=0

Wy multiply elements

2160w^2+66w=0

a = 2160; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·2160·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*2160}=\frac{-132}{4320}
=-11/360
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*2160}=\frac{0}{4320}
=0
$