52=(x+6)(x+5)

Solution for 52=(x+6)(x+5) equation:

52=(x+6)(x+5)

We move all terms to the left:

52-((x+6)(x+5))=0

We multiply parentheses ..

-((+x^2+5x+6x+30))+52=0


We calculate terms in parentheses: -((+x^2+5x+6x+30)), so:

(+x^2+5x+6x+30)

We get rid of parentheses

x^2+5x+6x+30

We add all the numbers together, and all the variables

x^2+11x+30

Back to the equation:

-(x^2+11x+30)


We get rid of parentheses

-x^2-11x-30+52=0

We add all the numbers together, and all the variables

-1x^2-11x+22=0

a = -1; b = -11; c = +22;
Δ = b2-4ac
Δ = -112-4·(-1)·22
Δ = 209
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{-(-11)-\sqrt{209}}{2*-1}=\frac{11-\sqrt{209}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{209}}{2*-1}=\frac{11+\sqrt{209}}{-2}
$