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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w-5)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-135w)/54w^2+(-2w)/54w^2+(-14w)/54w^2+5=0

We multiply all the terms by the denominator


(-135w)+(-2w)+(-14w)+5*54w^2=0

Wy multiply elements

270w^2+(-135w)+(-2w)+(-14w)=0

We get rid of parentheses

270w^2-135w-2w-14w=0

We add all the numbers together, and all the variables

270w^2-151w=0

a = 270; b = -151; c = 0;
Δ = b2-4ac
Δ = -1512-4·270·0
Δ = 22801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22801}=151$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-151)-151}{2*270}=\frac{0}{540}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-151)+151}{2*270}=\frac{302}{540}
=151/270
$