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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+34x-2=0

a = -2; b = 34; c = -2;
Δ = b2-4ac
Δ = 342-4·(-2)·(-2)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{285}}{2*-2}=\frac{-34-2\sqrt{285}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{285}}{2*-2}=\frac{-34+2\sqrt{285}}{-4}
$