3/x1=4/x+4

Solution for 3/x1=4/x+4 equation:

3/x1=4/x+4

We move all terms to the left:

3/x1-(4/x+4)=0


Domain of the equation: x1!=0

x^1!=0/

x^1!=√0

x!=0

x∈R



Domain of the equation: x+4)!=0

x∈R


We get rid of parentheses

3/x1-4/x-4=0

We calculate fractions


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

We multiply all the terms by the denominator


3x+(-4x)-4*x^2=0

We add all the numbers together, and all the variables

-4x^2+3x+(-4x)=0

We get rid of parentheses

-4x^2+3x-4x=0

We add all the numbers together, and all the variables

-4x^2-1x=0

a = -4; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-4)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-4}=\frac{2}{-8}
=-1/4
$