x^2=5(x-1)

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



x^2=5(x-1)

We move all terms to the left:

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



We calculate terms in parentheses: -(5(x-1)), so:

5(x-1)

We multiply parentheses

5x-5

Back to the equation:

-(5x-5)



We get rid of parentheses

x^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}
$

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