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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

4(2x-4)

We multiply parentheses

8x-16

Back to the equation:

-(8x-16)


We get rid of parentheses

-2x^2+10x-8x+16+4=0

We add all the numbers together, and all the variables

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

a = -2; b = 2; c = +20;
Δ = b2-4ac
Δ = 22-4·(-2)·20
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{41}}{2*-2}=\frac{-2-2\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{41}}{2*-2}=\frac{-2+2\sqrt{41}}{-4}
$