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

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

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

We move all terms to the left:

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


Domain of the equation: 4xx!=0

x!=0/1

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

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

We get rid of parentheses

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

We calculate fractions


(-448x^2)/2352x^2+768x^2/2352x^2+588x/2352x^2+(-1764x)/2352x^2=0

We multiply all the terms by the denominator


(-448x^2)+768x^2+588x+(-1764x)=0

We add all the numbers together, and all the variables

768x^2+(-448x^2)+588x+(-1764x)=0

We get rid of parentheses

768x^2-448x^2+588x-1764x=0

We add all the numbers together, and all the variables

320x^2-1176x=0

a = 320; b = -1176; c = 0;
Δ = b2-4ac
Δ = -11762-4·320·0
Δ = 1382976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1382976}=1176$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1176)-1176}{2*320}=\frac{0}{640}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1176)+1176}{2*320}=\frac{2352}{640}
=3+27/40
$