4+7/3x=-4+1/4x

Solution for 4+7/3x=-4+1/4x equation:

4+7/3x=-4+1/4x

We move all terms to the left:

4+7/3x-(-4+1/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/3x-(1/4x-4)+4=0

We get rid of parentheses

7/3x-1/4x+4+4=0

We calculate fractions


28x/12x^2+(-3x)/12x^2+4+4=0

We add all the numbers together, and all the variables

28x/12x^2+(-3x)/12x^2+8=0

We multiply all the terms by the denominator


28x+(-3x)+8*12x^2=0

Wy multiply elements

96x^2+28x+(-3x)=0

We get rid of parentheses

96x^2+28x-3x=0

We add all the numbers together, and all the variables

96x^2+25x=0

a = 96; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·96·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*96}=\frac{-50}{192}
=-25/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*96}=\frac{0}{192}
=0
$