x+(12/x)=7

Solution for x+(12/x)=7 equation:

x+(12/x)=7

We move all terms to the left:

x+(12/x)-(7)=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 get rid of parentheses

x+12/x-7=0

We multiply all the terms by the denominator


x*x-7*x+12=0

We add all the numbers together, and all the variables

-7x+x*x+12=0

Wy multiply elements

x^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{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*1}=\frac{8}{2}
=4
$