(X+1)(x+2)=66

Solution for (X+1)(x+2)=66 equation:

(X+1)(X+2)=66

We move all terms to the left:

(X+1)(X+2)-(66)=0

We multiply parentheses ..

(+X^2+2X+X+2)-66=0

We get rid of parentheses

X^2+2X+X+2-66=0

We add all the numbers together, and all the variables

X^2+3X-64=0

a = 1; b = 3; c = -64;
Δ = b2-4ac
Δ = 32-4·1·(-64)
Δ = 265
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{-(3)-\sqrt{265}}{2*1}=\frac{-3-\sqrt{265}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{265}}{2*1}=\frac{-3+\sqrt{265}}{2}
$