7/x=x-36

Solution for 7/x=x-36 equation:

7/x=x-36

We move all terms to the left:

7/x-(x-36)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

7/x-x+36=0

We multiply all the terms by the denominator


-x*x+36*x+7=0

We add all the numbers together, and all the variables

36x-x*x+7=0

Wy multiply elements

-1x^2+36x+7=0

a = -1; b = 36; c = +7;
Δ = b2-4ac
Δ = 362-4·(-1)·7
Δ = 1324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1324}=\sqrt{4*331}=\sqrt{4}*\sqrt{331}=2\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{331}}{2*-1}=\frac{-36-2\sqrt{331}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{331}}{2*-1}=\frac{-36+2\sqrt{331}}{-2}
$