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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2+2x+7x+14)), so:

(+x^2+2x+7x+14)

We get rid of parentheses

x^2+2x+7x+14

We add all the numbers together, and all the variables

x^2+9x+14

Back to the equation:

-(x^2+9x+14)


We get rid of parentheses

-x^2-9x-14+66=0

We add all the numbers together, and all the variables

-1x^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{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+17}{2*-1}=\frac{26}{-2}
=-13
$