(X+2)(x-7)=52

Solution for (X+2)(x-7)=52 equation:

(X+2)(X-7)=52

We move all terms to the left:

(X+2)(X-7)-(52)=0

We multiply parentheses ..

(+X^2-7X+2X-14)-52=0

We get rid of parentheses

X^2-7X+2X-14-52=0

We add all the numbers together, and all the variables

X^2-5X-66=0

a = 1; b = -5; c = -66;
Δ = b2-4ac
Δ = -52-4·1·(-66)
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{-(-5)-17}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*1}=\frac{22}{2}
=11
$