9/4w-3/5w=-13/40

Solution for 9/4w-3/5w=-13/40 equation:

9/4w-3/5w=-13/40

We move all terms to the left:

9/4w-3/5w-(-13/40)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We get rid of parentheses

9/4w-3/5w+13/40=0

We calculate fractions


1300w^2/3200w^2+7200w/3200w^2+(-1920w)/3200w^2=0

We multiply all the terms by the denominator


1300w^2+7200w+(-1920w)=0

We get rid of parentheses

1300w^2+7200w-1920w=0

We add all the numbers together, and all the variables

1300w^2+5280w=0

a = 1300; b = 5280; c = 0;
Δ = b2-4ac
Δ = 52802-4·1300·0
Δ = 27878400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27878400}=5280$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5280)-5280}{2*1300}=\frac{-10560}{2600}
=-4+4/65
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5280)+5280}{2*1300}=\frac{0}{2600}
=0
$