36=(x+1)(x+4)

Solution for 36=(x+1)(x+4) equation:

36=(x+1)(x+4)

We move all terms to the left:

36-((x+1)(x+4))=0

We multiply parentheses ..

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


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

(+x^2+4x+x+4)

We get rid of parentheses

x^2+4x+x+4

We add all the numbers together, and all the variables

x^2+5x+4

Back to the equation:

-(x^2+5x+4)


We get rid of parentheses

-x^2-5x-4+36=0

We add all the numbers together, and all the variables

-1x^2-5x+32=0

a = -1; b = -5; c = +32;
Δ = b2-4ac
Δ = -52-4·(-1)·32
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*-1}=\frac{5-3\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*-1}=\frac{5+3\sqrt{17}}{-2}
$