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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w+5)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


256w/192w^2+21w/192w^2+(-9w)/192w^2-5=0

We multiply all the terms by the denominator


256w+21w+(-9w)-5*192w^2=0

We add all the numbers together, and all the variables

277w+(-9w)-5*192w^2=0

Wy multiply elements

-960w^2+277w+(-9w)=0

We get rid of parentheses

-960w^2+277w-9w=0

We add all the numbers together, and all the variables

-960w^2+268w=0

a = -960; b = 268; c = 0;
Δ = b2-4ac
Δ = 2682-4·(-960)·0
Δ = 71824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{71824}=268$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(268)-268}{2*-960}=\frac{-536}{-1920}
=67/240
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(268)+268}{2*-960}=\frac{0}{-1920}
=0
$