-2/5w-5/3=7/3w-1

Solution for -2/5w-5/3=7/3w-1 equation:

-2/5w-5/3=7/3w-1

We move all terms to the left:

-2/5w-5/3-(7/3w-1)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w-1)!=0

w∈R


We get rid of parentheses

-2/5w-7/3w+1-5/3=0

We calculate fractions


(-54w)/135w^2+(-35w)/135w^2+(-25w)/135w^2+1=0

We multiply all the terms by the denominator


(-54w)+(-35w)+(-25w)+1*135w^2=0

Wy multiply elements

135w^2+(-54w)+(-35w)+(-25w)=0

We get rid of parentheses

135w^2-54w-35w-25w=0

We add all the numbers together, and all the variables

135w^2-114w=0

a = 135; b = -114; c = 0;
Δ = b2-4ac
Δ = -1142-4·135·0
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-114}{2*135}=\frac{0}{270}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+114}{2*135}=\frac{228}{270}
=38/45
$