(x-4)(x-6)=15

Solution for (x-4)(x-6)=15 equation:

(x-4)(x-6)=15

We move all terms to the left:

(x-4)(x-6)-(15)=0

We multiply parentheses ..

(+x^2-6x-4x+24)-15=0

We get rid of parentheses

x^2-6x-4x+24-15=0

We add all the numbers together, and all the variables

x^2-10x+9=0

a = 1; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·1·9
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*1}=\frac{18}{2}
=9
$