(X-2)(x-6)=-3

Solution for (X-2)(x-6)=-3 equation:

(X-2)(X-6)=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+X^2-6X-2X+12)+3=0

We get rid of parentheses

X^2-6X-2X+12+3=0

We add all the numbers together, and all the variables

X^2-8X+15=0

a = 1; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*1}=\frac{6}{2}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*1}=\frac{10}{2}
=5
$