(X+2)(x+3)/2=x*x

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

(X+2)(X+3)/2=X*X

We move all terms to the left:

(X+2)(X+3)/2-(X*X)=0

We add all the numbers together, and all the variables

(X+2)(X+3)/2-(+X*X)=0

We get rid of parentheses

(X+2)(X+3)/2-X*X=0

We multiply parentheses ..

(+X^2+3X+2X+6)/2-X*X=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1X^2+5X+6=0

a = -1; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-1)·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-1}=\frac{-12}{-2}
=+6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-1}=\frac{2}{-2}
=-1
$