1/4x+5/3x-4=2-1/4x

Solution for 1/4x+5/3x-4=2-1/4x equation:

1/4x+5/3x-4=2-1/4x

We move all terms to the left:

1/4x+5/3x-4-(2-1/4x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

1/4x+5/3x-(-1/4x+2)-4=0

We get rid of parentheses

1/4x+5/3x+1/4x-2-4=0

We calculate fractions


(3x+1)/12x^2+20x/12x^2-2-4=0

We add all the numbers together, and all the variables

(3x+1)/12x^2+20x/12x^2-6=0

We multiply all the terms by the denominator


(3x+1)+20x-6*12x^2=0

We add all the numbers together, and all the variables

20x+(3x+1)-6*12x^2=0

Wy multiply elements

-72x^2+20x+(3x+1)=0

We get rid of parentheses

-72x^2+20x+3x+1=0

We add all the numbers together, and all the variables

-72x^2+23x+1=0

a = -72; b = 23; c = +1;
Δ = b2-4ac
Δ = 232-4·(-72)·1
Δ = 817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{817}}{2*-72}=\frac{-23-\sqrt{817}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{817}}{2*-72}=\frac{-23+\sqrt{817}}{-144}
$