(x-3)2=x(x-5)

Solution for (x-3)2=x(x-5) equation:

(x-3)2=x(x-5)

We move all terms to the left:

(x-3)2-(x(x-5))=0

We multiply parentheses

2x-(x(x-5))-6=0


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

x(x-5)

We multiply parentheses

x^2-5x

Back to the equation:

-(x^2-5x)


We get rid of parentheses

-x^2+2x+5x-6=0

We add all the numbers together, and all the variables

-1x^2+7x-6=0

a = -1; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·(-1)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*-1}=\frac{-2}{-2}
=1
$