7-x=12/x

Solution for 7-x=12/x equation:

7-x=12/x

We move all terms to the left:

7-x-(12/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-(+12/x)+7=0

We add all the numbers together, and all the variables

-1x-(+12/x)+7=0

We get rid of parentheses

-1x-12/x+7=0

We multiply all the terms by the denominator


-1x*x+7*x-12=0

We add all the numbers together, and all the variables

7x-1x*x-12=0

Wy multiply elements

-1x^2+7x-12=0

a = -1; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·(-1)·(-12)
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{-(7)-1}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-1}=\frac{-6}{-2}
=+3
$