X^2-39x=120

Solution for X^2-39x=120 equation:

X^2-39X=120

We move all terms to the left:

X^2-39X-(120)=0

a = 1; b = -39; c = -120;
Δ = b2-4ac
Δ = -392-4·1·(-120)
Δ = 2001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{2001}}{2*1}=\frac{39-\sqrt{2001}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{2001}}{2*1}=\frac{39+\sqrt{2001}}{2}
$