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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

4x-(2x(x-5))-8-4=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 add all the numbers together, and all the variables

4x-(2x^2-10x)-12=0

We get rid of parentheses

-2x^2+4x+10x-12=0

We add all the numbers together, and all the variables

-2x^2+14x-12=0

a = -2; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-2)·(-12)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-2}=\frac{-4}{-4}
=1
$