(x-14)x=120

Solution for (x-14)x=120 equation:

(x-14)x=120

We move all terms to the left:

(x-14)x-(120)=0

We multiply parentheses

x^2-14x-120=0

a = 1; b = -14; c = -120;
Δ = b2-4ac
Δ = -142-4·1·(-120)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*1}=\frac{40}{2}
=20
$