96=(x-3)(x+5)

Solution for 96=(x-3)(x+5) equation:

96=(x-3)(x+5)

We move all terms to the left:

96-((x-3)(x+5))=0

We multiply parentheses ..

-((+x^2+5x-3x-15))+96=0


We calculate terms in parentheses: -((+x^2+5x-3x-15)), so:

(+x^2+5x-3x-15)

We get rid of parentheses

x^2+5x-3x-15

We add all the numbers together, and all the variables

x^2+2x-15

Back to the equation:

-(x^2+2x-15)


We get rid of parentheses

-x^2-2x+15+96=0

We add all the numbers together, and all the variables

-1x^2-2x+111=0

a = -1; b = -2; c = +111;
Δ = b2-4ac
Δ = -22-4·(-1)·111
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{7}}{2*-1}=\frac{2-8\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{7}}{2*-1}=\frac{2+8\sqrt{7}}{-2}
$