360/x=x-26

Solution for 360/x=x-26 equation:

360/x=x-26

We move all terms to the left:

360/x-(x-26)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

360/x-x+26=0

We multiply all the terms by the denominator


-x*x+26*x+360=0

We add all the numbers together, and all the variables

26x-x*x+360=0

Wy multiply elements

-1x^2+26x+360=0

a = -1; b = 26; c = +360;
Δ = b2-4ac
Δ = 262-4·(-1)·360
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-46}{2*-1}=\frac{-72}{-2}
=+36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+46}{2*-1}=\frac{20}{-2}
=-10
$