(5-x)x=1

Solution for (5-x)x=1 equation:

(5-x)x=1

We move all terms to the left:

(5-x)x-(1)=0

We add all the numbers together, and all the variables

(-1x+5)x-1=0

We multiply parentheses

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

a = -1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-1)·(-1)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{21}}{2*-1}=\frac{-5-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21}}{2*-1}=\frac{-5+\sqrt{21}}{-2}
$