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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-((x-2)(x+4))+20=0

We multiply parentheses ..

-((+x^2+4x-2x-8))+20=0


We calculate terms in parentheses: -((+x^2+4x-2x-8)), so:

(+x^2+4x-2x-8)

We get rid of parentheses

x^2+4x-2x-8

We add all the numbers together, and all the variables

x^2+2x-8

Back to the equation:

-(x^2+2x-8)


We get rid of parentheses

-x^2-2x+8+20=0

We add all the numbers together, and all the variables

-1x^2-2x+28=0

a = -1; b = -2; c = +28;
Δ = b2-4ac
Δ = -22-4·(-1)·28
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*-1}=\frac{2-2\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*-1}=\frac{2+2\sqrt{29}}{-2}
$