(x-2)(2x+2)=4*9

Solution for (x-2)(2x+2)=4*9 equation:

(x-2)(2x+2)=4*9

We move all terms to the left:

(x-2)(2x+2)-(4*9)=0

We add all the numbers together, and all the variables

(x-2)(2x+2)-36=0

We multiply parentheses ..

(+2x^2+2x-4x-4)-36=0

We get rid of parentheses

2x^2+2x-4x-4-36=0

We add all the numbers together, and all the variables

2x^2-2x-40=0

a = 2; b = -2; c = -40;
Δ = b2-4ac
Δ = -22-4·2·(-40)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*2}=\frac{20}{4}
=5
$