5x^2-x-120=0

Solution for 5x^2-x-120=0 equation:

5x^2-x-120=0

We add all the numbers together, and all the variables

5x^2-1x-120=0

a = 5; b = -1; c = -120;
Δ = b2-4ac
Δ = -12-4·5·(-120)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*5}=\frac{-48}{10}
=-4+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*5}=\frac{50}{10}
=5
$