5x^2-4x-120=0

Solution for 5x^2-4x-120=0 equation:

5x^2-4x-120=0

a = 5; b = -4; c = -120;
Δ = b2-4ac
Δ = -42-4·5·(-120)
Δ = 2416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{151}}{2*5}=\frac{4-4\sqrt{151}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{151}}{2*5}=\frac{4+4\sqrt{151}}{10}
$