2x(x-1)=2(16-x)

Solution for 2x(x-1)=2(16-x) equation:

2x(x-1)=2(16-x)

We move all terms to the left:

2x(x-1)-(2(16-x))=0

We add all the numbers together, and all the variables

2x(x-1)-(2(-1x+16))=0

We multiply parentheses

2x^2-2x-(2(-1x+16))=0


We calculate terms in parentheses: -(2(-1x+16)), so:

2(-1x+16)

We multiply parentheses

-2x+32

Back to the equation:

-(-2x+32)


We get rid of parentheses

2x^2-2x+2x-32=0

We add all the numbers together, and all the variables

2x^2-32=0

a = 2; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·2·(-32)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*2}=\frac{16}{4}
=4
$