13x2-24x-120=0

Solution for 13x2-24x-120=0 equation:

13x^2-24x-120=0

a = 13; b = -24; c = -120;
Δ = b2-4ac
Δ = -242-4·13·(-120)
Δ = 6816
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:

$\sqrt{\Delta}=\sqrt{6816}=\sqrt{16*426}=\sqrt{16}*\sqrt{426}=4\sqrt{426}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{426}}{2*13}=\frac{24-4\sqrt{426}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{426}}{2*13}=\frac{24+4\sqrt{426}}{26}
$