x(x-14)=172

Solution for x(x-14)=172 equation:

x(x-14)=172

We move all terms to the left:

x(x-14)-(172)=0

We multiply parentheses

x^2-14x-172=0

a = 1; b = -14; c = -172;
Δ = b2-4ac
Δ = -142-4·1·(-172)
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{221}}{2*1}=\frac{14-2\sqrt{221}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{221}}{2*1}=\frac{14+2\sqrt{221}}{2}
$