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

Solution for 4/x-4-3/1-x=0 equation:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/x-7=0

We multiply all the terms by the denominator


-1x*x-7*x+4=0

We add all the numbers together, and all the variables

-7x-1x*x+4=0

Wy multiply elements

-1x^2-7x+4=0

a = -1; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-1)·4
Δ = 65
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{-(-7)-\sqrt{65}}{2*-1}=\frac{7-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*-1}=\frac{7+\sqrt{65}}{-2}
$