x*(x-14)=96

Solution for x*(x-14)=96 equation:

x(x-14)=96

We move all terms to the left:

x(x-14)-(96)=0

We multiply parentheses

x^2-14x-96=0

a = 1; b = -14; c = -96;
Δ = b2-4ac
Δ = -142-4·1·(-96)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{145}}{2*1}=\frac{14-2\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{145}}{2*1}=\frac{14+2\sqrt{145}}{2}
$