-5/2w-6/5=7/5w-2

Solution for -5/2w-6/5=7/5w-2 equation:

-5/2w-6/5=7/5w-2

We move all terms to the left:

-5/2w-6/5-(7/5w-2)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 5w-2)!=0

w∈R


We get rid of parentheses

-5/2w-7/5w+2-6/5=0

We calculate fractions


(-625w)/250w^2+(-14w)/250w^2+(-12w)/250w^2+2=0

We multiply all the terms by the denominator


(-625w)+(-14w)+(-12w)+2*250w^2=0

Wy multiply elements

500w^2+(-625w)+(-14w)+(-12w)=0

We get rid of parentheses

500w^2-625w-14w-12w=0

We add all the numbers together, and all the variables

500w^2-651w=0

a = 500; b = -651; c = 0;
Δ = b2-4ac
Δ = -6512-4·500·0
Δ = 423801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{423801}=651$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-651)-651}{2*500}=\frac{0}{1000}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-651)+651}{2*500}=\frac{1302}{1000}
=1+151/500
$