7-x=14-4/x

Solution for 7-x=14-4/x equation:

7-x=14-4/x

We move all terms to the left:

7-x-(14-4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(-4/x+14)+7=0

We add all the numbers together, and all the variables

-1x-(-4/x+14)+7=0

We get rid of parentheses

-1x+4/x-14+7=0

We multiply all the terms by the denominator


-1x*x-14*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}
$