(X+2)(x+3)=(5+2)(5+3)

Solution for (X+2)(x+3)=(5+2)(5+3) equation:

(X+2)(X+3)=(5+2)(5+3)

We move all terms to the left:

(X+2)(X+3)-((5+2)(5+3))=0

We add all the numbers together, and all the variables

(X+2)(X+3)-(78)=0

We add all the numbers together, and all the variables

(X+2)(X+3)-78=0

We multiply parentheses ..

(+X^2+3X+2X+6)-78=0

We get rid of parentheses

X^2+3X+2X+6-78=0

We add all the numbers together, and all the variables

X^2+5X-72=0

a = 1; b = 5; c = -72;
Δ = b2-4ac
Δ = 52-4·1·(-72)
Δ = 313
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{313}}{2*1}=\frac{-5-\sqrt{313}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{313}}{2*1}=\frac{-5+\sqrt{313}}{2}
$