(x-2)(x+6)=20(9)

Solution for (x-2)(x+6)=20(9) equation:

(x-2)(x+6)=20(9)

We move all terms to the left:

(x-2)(x+6)-(20(9))=0

determiningTheFunctionDomain
(x-2)(x+6)-209=0

We multiply parentheses ..

(+x^2+6x-2x-12)-209=0

We get rid of parentheses

x^2+6x-2x-12-209=0

We add all the numbers together, and all the variables

x^2+4x-221=0

a = 1; b = 4; c = -221;
Δ = b2-4ac
Δ = 42-4·1·(-221)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-30}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+30}{2*1}=\frac{26}{2}
=13
$