(x+7)*(x+2)=66

Solution for (x+7)*(x+2)=66 equation:

(x+7)(x+2)=66

We move all terms to the left:

(x+7)(x+2)-(66)=0

We multiply parentheses ..

(+x^2+2x+7x+14)-66=0

We get rid of parentheses

x^2+2x+7x+14-66=0

We add all the numbers together, and all the variables

x^2+9x-52=0

a = 1; b = 9; c = -52;
Δ = b2-4ac
Δ = 92-4·1·(-52)
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{-(9)-17}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*1}=\frac{8}{2}
=4
$