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

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

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

We move all terms to the left:

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


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

3/5w+3/4w+6=0

We calculate fractions


12w/20w^2+15w/20w^2+6=0

We multiply all the terms by the denominator


12w+15w+6*20w^2=0

We add all the numbers together, and all the variables

27w+6*20w^2=0

Wy multiply elements

120w^2+27w=0

a = 120; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·120·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*120}=\frac{-54}{240}
=-9/40
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*120}=\frac{0}{240}
=0
$