36/x+x=15

Solution for 36/x+x=15 equation:

36/x+x=15

We move all terms to the left:

36/x+x-(15)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+36/x-15=0

We multiply all the terms by the denominator


x*x-15*x+36=0

We add all the numbers together, and all the variables

-15x+x*x+36=0

Wy multiply elements

x^2-15x+36=0

a = 1; b = -15; c = +36;
Δ = b2-4ac
Δ = -152-4·1·36
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*1}=\frac{24}{2}
=12
$