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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(+X^2-3X-2X+6)+2X-5=0

We get rid of parentheses

X^2-3X-2X+2X+6-5=0

We add all the numbers together, and all the variables

X^2-3X+1=0

a = 1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·1·1
Δ = 5
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{5}}{2*1}=\frac{3-\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5}}{2*1}=\frac{3+\sqrt{5}}{2}
$