(x-2)(x-4)=5x(x-4)

Solution for (x-2)(x-4)=5x(x-4) equation:

(x-2)(x-4)=5x(x-4)

We move all terms to the left:

(x-2)(x-4)-(5x(x-4))=0

We multiply parentheses ..

(+x^2-4x-2x+8)-(5x(x-4))=0


We calculate terms in parentheses: -(5x(x-4)), so:

5x(x-4)

We multiply parentheses

5x^2-20x

Back to the equation:

-(5x^2-20x)


We get rid of parentheses

x^2-5x^2-4x-2x+20x+8=0

We add all the numbers together, and all the variables

-4x^2+14x+8=0

a = -4; b = 14; c = +8;
Δ = b2-4ac
Δ = 142-4·(-4)·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-18}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+18}{2*-4}=\frac{4}{-8}
=-1/2
$