-2x(x-4)-6=2x-16

Solution for -2x(x-4)-6=2x-16 equation:

-2x(x-4)-6=2x-16

We move all terms to the left:

-2x(x-4)-6-(2x-16)=0

We multiply parentheses

-2x^2+8x-(2x-16)-6=0

We get rid of parentheses

-2x^2+8x-2x+16-6=0

We add all the numbers together, and all the variables

-2x^2+6x+10=0

a = -2; b = 6; c = +10;
Δ = b2-4ac
Δ = 62-4·(-2)·10
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{29}}{2*-2}=\frac{-6-2\sqrt{29}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{29}}{2*-2}=\frac{-6+2\sqrt{29}}{-4}
$