(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^2-2x-39=0

a = 1; b = -2; c = -39;
Δ = b2-4ac
Δ = -22-4·1·(-39)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{10}}{2*1}=\frac{2-4\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{10}}{2*1}=\frac{2+4\sqrt{10}}{2}
$