(X-4)(x-3)=2

Solution for (X-4)(x-3)=2 equation:

(X-4)(X-3)=2

We move all terms to the left:

(X-4)(X-3)-(2)=0

We multiply parentheses ..

(+X^2-3X-4X+12)-2=0

We get rid of parentheses

X^2-3X-4X+12-2=0

We add all the numbers together, and all the variables

X^2-7X+10=0

a = 1; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*1}=\frac{10}{2}
=5
$