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

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

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

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


189w/108w^2+(-16w)/108w^2+(-28w)/108w^2+5=0

We multiply all the terms by the denominator


189w+(-16w)+(-28w)+5*108w^2=0

Wy multiply elements

540w^2+189w+(-16w)+(-28w)=0

We get rid of parentheses

540w^2+189w-16w-28w=0

We add all the numbers together, and all the variables

540w^2+145w=0

a = 540; b = 145; c = 0;
Δ = b2-4ac
Δ = 1452-4·540·0
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(145)-145}{2*540}=\frac{-290}{1080}
=-29/108
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(145)+145}{2*540}=\frac{0}{1080}
=0
$