4x+5=(x+1)(x+2)

Solution for 4x+5=(x+1)(x+2) equation:

4x+5=(x+1)(x+2)

We move all terms to the left:

4x+5-((x+1)(x+2))=0

We multiply parentheses ..

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


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

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

We get rid of parentheses

x^2+2x+x+2

We add all the numbers together, and all the variables

x^2+3x+2

Back to the equation:

-(x^2+3x+2)


We add all the numbers together, and all the variables

4x-(x^2+3x+2)+5=0

We get rid of parentheses

-x^2+4x-3x-2+5=0

We add all the numbers together, and all the variables

-1x^2+x+3=0

a = -1; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-1)·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{13}}{2*-1}=\frac{-1-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*-1}=\frac{-1+\sqrt{13}}{-2}
$