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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


500w/375w^2+3w/375w^2+(-9w)/375w^2+3=0

We multiply all the terms by the denominator


500w+3w+(-9w)+3*375w^2=0

We add all the numbers together, and all the variables

503w+(-9w)+3*375w^2=0

Wy multiply elements

1125w^2+503w+(-9w)=0

We get rid of parentheses

1125w^2+503w-9w=0

We add all the numbers together, and all the variables

1125w^2+494w=0

a = 1125; b = 494; c = 0;
Δ = b2-4ac
Δ = 4942-4·1125·0
Δ = 244036
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{244036}=494$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(494)-494}{2*1125}=\frac{-988}{2250}
=-494/1125
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(494)+494}{2*1125}=\frac{0}{2250}
=0
$