5/3w-5/3=-5/4w-6

Solution for 5/3w-5/3=-5/4w-6 equation:

5/3w-5/3=-5/4w-6

We move all terms to the left:

5/3w-5/3-(-5/4w-6)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w-6)!=0

w∈R


We get rid of parentheses

5/3w+5/4w+6-5/3=0

We calculate fractions


20w/108w^2+135w/108w^2+(-20w)/108w^2+6=0

We multiply all the terms by the denominator


20w+135w+(-20w)+6*108w^2=0

We add all the numbers together, and all the variables

155w+(-20w)+6*108w^2=0

Wy multiply elements

648w^2+155w+(-20w)=0

We get rid of parentheses

648w^2+155w-20w=0

We add all the numbers together, and all the variables

648w^2+135w=0

a = 648; b = 135; c = 0;
Δ = b2-4ac
Δ = 1352-4·648·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-135}{2*648}=\frac{-270}{1296}
=-5/24
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+135}{2*648}=\frac{0}{1296}
=0
$