-4/5w-4/5=1/3w-7

Solution for -4/5w-4/5=1/3w-7 equation:

-4/5w-4/5=1/3w-7

We move all terms to the left:

-4/5w-4/5-(1/3w-7)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w-7)!=0

w∈R


We get rid of parentheses

-4/5w-1/3w+7-4/5=0

We calculate fractions


(-180w^2)/375w^2+(-300w)/375w^2+(-125w)/375w^2+7=0

We multiply all the terms by the denominator


(-180w^2)+(-300w)+(-125w)+7*375w^2=0

Wy multiply elements

(-180w^2)+2625w^2+(-300w)+(-125w)=0

We get rid of parentheses

-180w^2+2625w^2-300w-125w=0

We add all the numbers together, and all the variables

2445w^2-425w=0

a = 2445; b = -425; c = 0;
Δ = b2-4ac
Δ = -4252-4·2445·0
Δ = 180625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{180625}=425$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-425)-425}{2*2445}=\frac{0}{4890}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-425)+425}{2*2445}=\frac{850}{4890}
=85/489
$