(x-2)(x+4)=(4)(5)

Solution for (x-2)(x+4)=(4)(5) equation:

(x-2)(x+4)=(4)(5)

We move all terms to the left:

(x-2)(x+4)-((4)(5))=0

determiningTheFunctionDomain
(x-2)(x+4)-45=0

We multiply parentheses ..

(+x^2+4x-2x-8)-45=0

We get rid of parentheses

x^2+4x-2x-8-45=0

We add all the numbers together, and all the variables

x^2+2x-53=0

a = 1; b = 2; c = -53;
Δ = b2-4ac
Δ = 22-4·1·(-53)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{6}}{2*1}=\frac{-2-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{6}}{2*1}=\frac{-2+6\sqrt{6}}{2}
$