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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2+10x-4x-20)-((2x-4))=0


We calculate terms in parentheses: -((2x-4)), so:

(2x-4)

We get rid of parentheses

2x-4

Back to the equation:

-(2x-4)


We get rid of parentheses

2x^2+10x-4x-2x-20+4=0

We add all the numbers together, and all the variables

2x^2+4x-16=0

a = 2; b = 4; c = -16;
Δ = b2-4ac
Δ = 42-4·2·(-16)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*2}=\frac{8}{4}
=2
$