(x+8)(x-2)=(x+2)*2

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

(x+8)(x-2)=(x+2)*2

We move all terms to the left:

(x+8)(x-2)-((x+2)*2)=0

We multiply parentheses ..

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


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

(x+2)*2

We multiply parentheses

2x+4

Back to the equation:

-(2x+4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+4x-20=0

a = 1; b = 4; c = -20;
Δ = b2-4ac
Δ = 42-4·1·(-20)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*1}=\frac{-4-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*1}=\frac{-4+4\sqrt{6}}{2}
$