x^2-120=-14x

Solution for x^2-120=-14x equation:

x^2-120=-14x

We move all terms to the left:

x^2-120-(-14x)=0

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