1/x+5=x-3/x+12

Solution for 1/x+5=x-3/x+12 equation:

1/x+5=x-3/x+12

We move all terms to the left:

1/x+5-(x-3/x+12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+12)!=0

x∈R


We get rid of parentheses

1/x-x+3/x-12+5=0

We multiply all the terms by the denominator


-x*x-12*x+5*x+1+3=0

We add all the numbers together, and all the variables

-7x-x*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}
$