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 calculate terms in parentheses: -(x(x-1)), so:

x(x-1)

We multiply parentheses

x^2-1x

Back to the equation:

-(x^2-1x)


We get rid of parentheses

-x^2+1x+5=0

We add all the numbers together, and all the variables

-1x^2+x+5=0

a = -1; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-1)·5
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{-(1)-\sqrt{21}}{2*-1}=\frac{-1-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*-1}=\frac{-1+\sqrt{21}}{-2}
$