5/4w-7/4=-2/3w-4

Solution for 5/4w-7/4=-2/3w-4 equation:

5/4w-7/4=-2/3w-4

We move all terms to the left:

5/4w-7/4-(-2/3w-4)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w-4)!=0

w∈R


We get rid of parentheses

5/4w+2/3w+4-7/4=0

We calculate fractions


15w/192w^2+128w/192w^2+(-21w)/192w^2+4=0

We multiply all the terms by the denominator


15w+128w+(-21w)+4*192w^2=0

We add all the numbers together, and all the variables

143w+(-21w)+4*192w^2=0

Wy multiply elements

768w^2+143w+(-21w)=0

We get rid of parentheses

768w^2+143w-21w=0

We add all the numbers together, and all the variables

768w^2+122w=0

a = 768; b = 122; c = 0;
Δ = b2-4ac
Δ = 1222-4·768·0
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-122}{2*768}=\frac{-244}{1536}
=-61/384
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+122}{2*768}=\frac{0}{1536}
=0
$