3+224=(x+4)(x-2)

Solution for 3+224=(x+4)(x-2) equation:

3+224=(x+4)(x-2)

We move all terms to the left:

3+224-((x+4)(x-2))=0

We add all the numbers together, and all the variables

-((x+4)(x-2))+227=0

We multiply parentheses ..

-((+x^2-2x+4x-8))+227=0


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

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

We get rid of parentheses

x^2-2x+4x-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+227=0

We add all the numbers together, and all the variables

-1x^2-2x+235=0

a = -1; b = -2; c = +235;
Δ = b2-4ac
Δ = -22-4·(-1)·235
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{59}}{2*-1}=\frac{2-4\sqrt{59}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{59}}{2*-1}=\frac{2+4\sqrt{59}}{-2}
$