(x+8)(x-2)=52+(x-4)2

Solution for (x+8)(x-2)=52+(x-4)2 equation:

(x+8)(x-2)=52+(x-4)2

We move all terms to the left:

(x+8)(x-2)-(52+(x-4)2)=0

We multiply parentheses ..

(+x^2-2x+8x-16)-(52+(x-4)2)=0


We calculate terms in parentheses: -(52+(x-4)2), so:

52+(x-4)2

determiningTheFunctionDomain
(x-4)2+52

We multiply parentheses

2x-8+52

We add all the numbers together, and all the variables

2x+44

Back to the equation:

-(2x+44)


We get rid of parentheses

x^2-2x+8x-2x-16-44=0

We add all the numbers together, and all the variables

x^2+4x-60=0

a = 1; b = 4; c = -60;
Δ = b2-4ac
Δ = 42-4·1·(-60)
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{-(4)-16}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*1}=\frac{12}{2}
=6
$