365/X=x-6

Solution for 365/X=x-6 equation:

365/X=X-6

We move all terms to the left:

365/X-(X-6)=0


Domain of the equation: X!=0

X∈R


We get rid of parentheses

365/X-X+6=0

We multiply all the terms by the denominator


-X*X+6*X+365=0

We add all the numbers together, and all the variables

6X-X*X+365=0

Wy multiply elements

-1X^2+6X+365=0

a = -1; b = 6; c = +365;
Δ = b2-4ac
Δ = 62-4·(-1)·365
Δ = 1496
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:

$\sqrt{\Delta}=\sqrt{1496}=\sqrt{4*374}=\sqrt{4}*\sqrt{374}=2\sqrt{374}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{374}}{2*-1}=\frac{-6-2\sqrt{374}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{374}}{2*-1}=\frac{-6+2\sqrt{374}}{-2}
$