5(x-1)=x^2

Solution for 5(x-1)=x^2 equation:

5(x-1)=x^2

We move all terms to the left:

5(x-1)-(x^2)=0

determiningTheFunctionDomain
-x^2+5(x-1)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

a = -1; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·(-1)·(-5)
Δ = 5
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{5}}{2*-1}=\frac{-5-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{5}}{2*-1}=\frac{-5+\sqrt{5}}{-2}
$