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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-(2x(x-5))-10=0


We calculate terms in parentheses: -(2x(x-5)), so:

2x(x-5)

We multiply parentheses

2x^2-10x

Back to the equation:

-(2x^2-10x)


We get rid of parentheses

-2x^2+2x+10x-10=0

We add all the numbers together, and all the variables

-2x^2+12x-10=0

a = -2; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·(-2)·(-10)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*-2}=\frac{-4}{-4}
=1
$