7+4/9w=3-5/6w

Solution for 7+4/9w=3-5/6w equation:

7+4/9w=3-5/6w

We move all terms to the left:

7+4/9w-(3-5/6w)=0


Domain of the equation: 9w!=0

w!=0/9

w!=0

w∈R



Domain of the equation: 6w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

4/9w-(-5/6w+3)+7=0

We get rid of parentheses

4/9w+5/6w-3+7=0

We calculate fractions


24w/54w^2+45w/54w^2-3+7=0

We add all the numbers together, and all the variables

24w/54w^2+45w/54w^2+4=0

We multiply all the terms by the denominator


24w+45w+4*54w^2=0

We add all the numbers together, and all the variables

69w+4*54w^2=0

Wy multiply elements

216w^2+69w=0

a = 216; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·216·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*216}=\frac{-138}{432}
=-23/72
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*216}=\frac{0}{432}
=0
$