52=(x+4)(x-5)

Solution for 52=(x+4)(x-5) equation:

52=(x+4)(x-5)

We move all terms to the left:

52-((x+4)(x-5))=0

We multiply parentheses ..

-((+x^2-5x+4x-20))+52=0


We calculate terms in parentheses: -((+x^2-5x+4x-20)), so:

(+x^2-5x+4x-20)

We get rid of parentheses

x^2-5x+4x-20

We add all the numbers together, and all the variables

x^2-1x-20

Back to the equation:

-(x^2-1x-20)


We get rid of parentheses

-x^2+1x+20+52=0

We add all the numbers together, and all the variables

-1x^2+x+72=0

a = -1; b = 1; c = +72;
Δ = b2-4ac
Δ = 12-4·(-1)·72
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-1}=\frac{16}{-2}
=-8
$