-2x(x-8)=4(x+1)

Solution for -2x(x-8)=4(x+1) equation:

-2x(x-8)=4(x+1)

We move all terms to the left:

-2x(x-8)-(4(x+1))=0

We multiply parentheses

-2x^2+16x-(4(x+1))=0


We calculate terms in parentheses: -(4(x+1)), so:

4(x+1)

We multiply parentheses

4x+4

Back to the equation:

-(4x+4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·(-2)·(-4)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*-2}=\frac{-12-4\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*-2}=\frac{-12+4\sqrt{7}}{-4}
$