x(x-7)=120

Solution for x(x-7)=120 equation:

x(x-7)=120

We move all terms to the left:

x(x-7)-(120)=0

We multiply parentheses

x^2-7x-120=0

a = 1; b = -7; c = -120;
Δ = b2-4ac
Δ = -72-4·1·(-120)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*1}=\frac{30}{2}
=15
$