(X+2)(x+3)=182

Solution for (X+2)(x+3)=182 equation:

(X+2)(X+3)=182

We move all terms to the left:

(X+2)(X+3)-(182)=0

We multiply parentheses ..

(+X^2+3X+2X+6)-182=0

We get rid of parentheses

X^2+3X+2X+6-182=0

We add all the numbers together, and all the variables

X^2+5X-176=0

a = 1; b = 5; c = -176;
Δ = b2-4ac
Δ = 52-4·1·(-176)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-27}{2*1}=\frac{-32}{2}
=-16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+27}{2*1}=\frac{22}{2}
=11
$