13x^2-12x-60=0

Solution for 13x^2-12x-60=0 equation:

13x^2-12x-60=0

a = 13; b = -12; c = -60;
Δ = b2-4ac
Δ = -122-4·13·(-60)
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{51}}{2*13}=\frac{12-8\sqrt{51}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{51}}{2*13}=\frac{12+8\sqrt{51}}{26}
$