124/x=x+27

Solution for 124/x=x+27 equation:

124/x=x+27

We move all terms to the left:

124/x-(x+27)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

124/x-x-27=0

We multiply all the terms by the denominator


-x*x-27*x+124=0

We add all the numbers together, and all the variables

-27x-x*x+124=0

Wy multiply elements

-1x^2-27x+124=0

a = -1; b = -27; c = +124;
Δ = b2-4ac
Δ = -272-4·(-1)·124
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-35}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+35}{2*-1}=\frac{62}{-2}
=-31
$