(X+2)(x+3)=40

Solution for (X+2)(x+3)=40 equation:

(X+2)(X+3)=40

We move all terms to the left:

(X+2)(X+3)-(40)=0

We multiply parentheses ..

(+X^2+3X+2X+6)-40=0

We get rid of parentheses

X^2+3X+2X+6-40=0

We add all the numbers together, and all the variables

X^2+5X-34=0

a = 1; b = 5; c = -34;
Δ = b2-4ac
Δ = 52-4·1·(-34)
Δ = 161
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{-(5)-\sqrt{161}}{2*1}=\frac{-5-\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{161}}{2*1}=\frac{-5+\sqrt{161}}{2}
$