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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w-7)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-20w)/135w^2+27w/135w^2+5w/135w^2+7=0

We multiply all the terms by the denominator


(-20w)+27w+5w+7*135w^2=0

We add all the numbers together, and all the variables

32w+(-20w)+7*135w^2=0

Wy multiply elements

945w^2+32w+(-20w)=0

We get rid of parentheses

945w^2+32w-20w=0

We add all the numbers together, and all the variables

945w^2+12w=0

a = 945; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·945·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*945}=\frac{-24}{1890}
=-4/315
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*945}=\frac{0}{1890}
=0
$