234/x=x+5

Solution for 234/x=x+5 equation:

234/x=x+5

We move all terms to the left:

234/x-(x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

234/x-x-5=0

We multiply all the terms by the denominator


-x*x-5*x+234=0

We add all the numbers together, and all the variables

-5x-x*x+234=0

Wy multiply elements

-1x^2-5x+234=0

a = -1; b = -5; c = +234;
Δ = b2-4ac
Δ = -52-4·(-1)·234
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-31}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+31}{2*-1}=\frac{36}{-2}
=-18
$